Free Printable Probability of Combined Events

1.

Which of the following is correct?

a)

_{n(S) = n(A) X n(B)}

b)

n(S) = n(A) + n(B)

c)

n(S) = n(A) - n(B)

d)

n(S) = n(A) / n(B)

2.

How many sample space are there for the combined event below?

'Adham (A) and Nafeez (N) play a maximum of five badminton matches. The player that wins three sets is the winner'

a)

12

b)

20

c)

25

3.

Which of the following is/are dependent events?

a)

The pointer of a lucky wheel stops at the same sector twice consecutively

b)

The selection of two boys from a group of ten girls and fourteen boys at random

c)

Answer three objective questions with four options correctly if the answer of each question is chosen at random

d)

Obtain two pens of the same colour when two pens are taken out at random from a container that contains 3 red pens and 2 blue pens with replacement.

4.

Box A contains a red card and two yellow cards.

Box B contains three red cards and a yellow card.

Fauziah chooses a card from box A and box B respectively.

What are the probability of Fauziah getting both yellow cards?

a)

1/6

b)

2/3

c)

1/4

d)

2/9

5.

According to an investigation, the probability of rainfall on Mountain X in May is 0.45.

Calculate the probability that Mountain X will have two consecutive rainy days in May.

a)

0.90

b)

0.55

c)

0.3025

d)

0.2025

6.

A box contains 12 bulbs where two of the bulbs are burnt. Two bulbs are selected at random from the box.

Calculate the probability of getting two burnt bulbs.

a)

1/36

b)

1/66

c)

15/22

d)

25/36

7.

Which of the following is/are the addition rule of probability?

a)

b)

c)

d)

8.

The probability that a smartphone manufactured has a display problem is 2/13. Two smartphones are chosen at random.

Calculate the probability that at least one smartphone chosen has a display problem.

a)

48/169

b)

121/169

c)

4/169

d)

44/169

9.

Seven cards labelled with the letters "G,E,M,B,I,R,A" are put in a box. A card is chosen at random from the box.

Calculate the probability that the card chosen is labelled with a vowel or letter "R"

a)

4/7

b)

12/49

c)

3/7

d)

37/49

10.

a)

1/5

b)

1/15

c)

1/20

d)

0

11.

a)

1/30

b)

2/15

c)

7/30

d)

8/30

12.

Two prefects are chosen at random from five prefects, where three of them are in Form Four and two are in Form Five.

Calculate the probability that both prefects chosen are in the same form.

a)

0.09

b)

0.6

c)

0.10

d)

0.4

13.

a)

43/200

b)

35/200

c)

105/200

d)

None of the above

14.

The probability of Kam Seng passing his Physics and Chemistry tests are 0.58 and 0.42 respectively.

Calculate the probability that

a) Kam Seng passes both tests.

a)

0.2345

b)

0.2436

c)

0.2433

d)

0.2536

15.

The probability of Kam Seng passing his Physics and Chemistry tests are 0.58 and 0.42 respectively.

Calculate the probability that

b) Kam Seng passes only one test

a)

0.4128

b)

0.5

c)

0.5128

d)

0.5118

16.

The probabilities of Kam Seng passing in Science and Mathematics subjects are 0.78 and 0.56 respectively. Calculate the probability that at least one subject is passed.

a)

0.9032

b)

0.5336

c)

0.4664

d)

0.4368

17.

A number is chosen at random from theset S = {x: x is an integer, $1\le x\le50$ }.
Calculate the probability of getting a factor number of 20 or a multiple of 8.

a)

$\frac{12}{50}$

b)

$\frac{13}{50}$

c)

$\frac{8}{25}$

d)

$\frac{6}{25}$

18.

Athletes M and N are involved in a 100 meter sprint race. If the probabilities of athletes M and N respectively passing the specified conditions are $\frac{4}{5}\ and\ \frac{5}{6},$ find the probability that only one of the athletes successfully passes them.

a)

$\frac{2}{3}$

b)

$\frac{1}{6}$

c)

$\frac{3}{10}$

d)

$\frac{2}{15}$

19.

Mark has eight pencils and three of them are blue. 40% of the pencils Farhan owns are blue. $\frac{1}{5}$ of the pencils owned by Suresh are blue. Mark, Farhan and Suresh each choose a pencil at random.
Calculate the probability that at least two of them will choose a blue pencil.

a)

$\frac{3}{25}$

b)

$\frac{3}{100}$

c)

$\frac{43}{200}$

d)

$\frac{49}{200}$

20.

Event C and D are independent where P(C) = 0.96 and

P(C ∩ D) = 0.36.

Find P(D).

a)

0.306

b)

0.323

c)

0.346

d)

0.375

21.

Five cards labelled with the letters "R, A, J, I, N" are put into a box. Two cards are taken out at random from the box one by one without replacement.

Which of the following is not the possible outcome for the event?

a)

(I, J)

b)

(J, J)

c)

(I, N)

d)

(R, A)

22.

The diagram shows the cards in box M and box N. A card is chosen at random from each of the boxes.

Calculate the probability of getting a perfect square and a vowel.

a)

$\frac{1}{6}$

b)

$\frac{1}{4}$

c)

$\frac{3}{4}$

d)

$\frac{1}{2}$

23.

The probability of a patient is infected with a virus is $\frac{1}{10}.$

Two patients are selected at random to perform the screening at the same time.

Calculate the probability that at least one of the patients selected is infected with the virus.

a)

$\frac{1}{10}$

b)

$\frac{9}{50}$

c)

$\frac{19}{100}$

d)

$\frac{81}{100}$

24.

The cards labelled with the letters

"K, E, B, O, L, E, H, J, A, D, I, A, N" are put in a container.

Determine $P\left(R\cup T\right).$

a)

$\frac{6}{13}$

b)

$\frac{7}{13}$

c)

$\frac{8}{13}$

d)

$\frac{9}{13}$

25.

Good Pizza Shop has sold 12 pieces of Chicago pizza, 8 pieces of Italian pizza and x pieces of New York pizza in one day. A piece of pizza is chosen at random, the probability of a piece of Chicago pizza or a piece of New York pizza being chosen is $\frac{11}{15}$ .
Calculate the value of x.

a)

8

b)

9

c)

10

d)

12

26.

What is the sample spaces for the combined event below:

Two books are chosen at random from a bookshelf that contains a history book (H), two mathematics books (M) and a geography book (G)

a)

{(H,M1),(H,M2),(H,G),(M1,M2),(M1,G),(M2,G)}

b)

(H,M1),(H,M2),(H,G),(M1,H),(M1,M2),(M1,G),(M2,H),(M2,M1),(M2,G),(G,H),(G,M1),(G,M2)

c)

{(H,M1),(H,M2),(H,G),(M1,H),(M1,M2),(M1,G),(M2,H),(M2,M1),(M2,G),(G,H),(G,M1),(G,M2)}

d)

(H,M1),(H,M2),(H,G),(M1,M2),(M1,G),(M2,G)

27.

Determine whether the following event is dependent event or independent event:

Vincent and Bajat sit for a Mathematics test in school. Vincent and Bajat pass the Mathematics test.

a)

INDEPENDENT EVENT

b)

DEPENDENT EVENT

28.

Box A contains a red card and two yellow cards. Box B contains three red cards and a yellow card. Nelly chooses a card from Box A and Box B respectively. Calculate the probability that Nelly gets two yellow cards.

a)

$\frac{11}{12}$

b)

$\frac{1}{6}$

c)

$\frac{3}{7}$

d)

$\frac{1}{12}$

29.

Box K and Box L contain four cards labelled with the letter "L,I,K,E" and three cards labelled with the numbers "5,6,7" respectively. A card is chosen at random from Box K and Box L respectively. Calculate the probability of getting a vowel and an even number.

a)

$\frac{2}{3}$

b)

$\frac{1}{3}$

c)

$\frac{5}{6}$

d)

$\frac{1}{6}$

30.

A fair dice with four faces is labelled "1,2,3,4". The dice is rolled twice and the numbers that the dice lands on are recorded. By listing all the possible outcomes, calculate the probability of getting two odd numbers.

a)

$\frac{1}{4}$

b)

$\frac{3}{4}$

c)

$\frac{1}{2}$

d)

1

31.

A coin is tossed and a dice is rolled simultaneously. By listing the sample of all the possible outcomes of the event, find the probability that a head and an odd number are obtained?

a)

$\frac{2}{3}$

b)

$\frac{3}{4}$

c)

$\frac{1}{4}$

d)

$\frac{1}{3}$

32.

A coin is tossed and a dice is rolled simultaneously. By listing the sample of all the possible outcomes of the event, find the probability that a head or a number greater than 4 are obtained.

a)

$\frac{1}{4}$

b)

$\frac{1}{3}$

c)

$\frac{3}{4}$

d)

$\frac{2}{3}$

33.

Seven cards labelled with the letters "B,A,H,A,G,I,A" are put in a box. A card is chosen at random.

L is the event of getting a vowel

M is the event of getting a consonant

N is the event of getting a letter "B"

Calculate the probability of combined event L or N to occur.

a)

$\frac{5}{7}$

b)

$\frac{18}{49}$

c)

$\frac{2}{7}$

d)

$\frac{31}{49}$

34.

Eight cards labelled with the letters "T,H,U,R,S,D,A,Y" are put in a box. A card is chosen at random from the box. Calculate the probability that the card chosen is labelled with a vowel or letter "R".

a)

$\frac{3}{4}$

b)

$\frac{5}{8}$

c)

$\frac{1}{4}$

d)

$\frac{3}{8}$

35.

The probability of appointing Adam as the chairman of the Finance Club (F) and the head of the sports house (S) are $\frac{3}{5}$ and $\frac{2}{9}$ respectively. Calculate the probability of not appointing Adam as the chairman of the Finance Club (F) or the head of the sports house (S)

a)

$\frac{37}{72}$

b)

$\frac{5}{36}$

c)

$\frac{7}{24}$

d)

$\frac{35}{72}$

36.

Box R contains five red marbles and seven green marbles while Box T contains four red marbles and eight green marbles.

A marble is randomly selected from Box R. If the marble is red, that marble will be put into box T. If the marble is green, that marble will be returned to Box R.

Then, a marble will be randomly selected from Box T. The colors of the selected marble will be recorded.

Calculate the probability of selecting two red marbles.

a)

$\frac{20}{156}$

b)

$\frac{25}{156}$

c)

$\frac{131}{156}$

d)

$\frac{136}{156}$

37.

Box R contains five red marbles and seven green marbles while Box T contains four red marbles and eight green marbles.

A marble is randomly selected from Box R. If the marble is red, that marble will be put into box T. If the marble is green, that marble will be returned to Box R.

Then, a marble will be randomly selected from Box T. The colors of the selected marble will be recorded.

Calculate the probability of selecting two marbles of different colors.

a)

$\frac{300}{468}$

b)

$\frac{257}{468}$

c)

$\frac{211}{468}$

d)

$\frac{168}{468}$

38.

Pia has eight shirts and three of them are blue shirts. 40% of the shirts that Yana has are blue. $\frac{1}{5}$ of the shirts that Mei Mei has are blue. Pia, Yana and Mei Mei each chooses a shirt at random to attend ad meeting. Calculate the probability that two of them wear blue shirts.

a)

$\frac{139}{200}$

b)

$\frac{43}{200}$

c)

$\frac{61}{200}$

d)

$\frac{157}{200}$

39.

The tree diagram shows the outcomes of rolling a die and flipping a coin.
What is the probability of rolling an even number and flipping a head?

a)

³/₁₂

b)

¹/₂

c)

⁴/₁₂

d)

⁰/₁₂

40.

The tree diagram shows the outcomes of rolling a die and flipping a coin.
How many total outcomes are there?

a)

6

b)

12

c)

24

d)

36

41.

The cafeteria is serving three kinds of sandwiches: tuna (T), chicken, (C), and peanut butter (P). They are also serving a choice of two drinks: milk (M) or water (W). Which shows the complete set of possible combinations?

a)

TW, CW, PW

b)

TW, TM, TC, CW, PW

c)

TW, TM, CW, CM, PW, PM

d)

TCP, MW

42.

What is the probability that you will get plain crust with ham on your pizza?

a)

1/8

b)

1/₂

c)

1/₁₀

d)

2/₁₀

43.

Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. Find the probability of selecting one green marble from bag A and one black marble from bag B.

a)

3/20

b)

1/4

c)

3/31

d)

2/27

44.

A bag contains 9 green marbles, 5 yellow marbles and 6 red marbles. You choose one marble. What is the probability of selecting a green or red marble?

a)

8/15

b)

6/11

c)

3/4

d)

2/3

45.

You pick a marble from this bag.
What is the probability you will choose either a black or white marble?

a)

3/5

b)

9/100

c)

1/10

d)

2/5

46.

In a badminton tournament, the Malaysia team plays against the China team and the Indonesia team plays against the Thailand team. The probability that the Malaysia team wins against the China team is $\frac{1}{3}$ . The probability that the Indonesia team wins against the Thailand team is $\frac{2}{3}$ . Find the probability that both the Malaysia team and the Indonesia team lose their games.

a)

$\frac{1}{3}$

b)

$\frac{2}{3}$

c)

$\frac{2}{9}$

d)

$\frac{5}{9}$

47.

Seven cards labelled with the letters "G,E,M,B,I,R,A" are put in a box. A card is chosen at random from the box.

Calculate the probability that the card chosen is labelled with a vowel or letter "R"

a)

4/7

b)

12/49

c)

3/7

d)

37/49

48.

A box contains 12 bulbs where two of the bulbs are burnt. Two bulbs are selected at random from the box.

Calculate the probability of getting two burnt bulbs.

a)

1/36

b)

1/66

c)

15/22

d)

25/36

49.

a)

A

b)

B

c)

C

d)

D

50.

a)

A

b)

B

c)

C

d)

D

51.

a)

A

b)

B

c)

C

d)

D

52.

a)

A

b)

B

c)

C

d)

D

53.

a)

A

b)

B

c)

C

d)

D

54.

a)

A

b)

B

c)

C

d)

D

55.

a)

A

b)

B

c)

C

d)

D

56.

a)

A

b)

B

c)

C

d)

D

57.

Danny has 20 chocolates. 5 are milk chocolates, 10 are dark chocolates, and 5 are white chocolates. What is the probability of getting a milk chocolate or a dark chocolate?

a)

3/4

b)

1/2

c)

1/15

d)

3/10

58.

a)

A

b)

B

c)

C

d)

D

59.

a)

A

b)

B

c)

C

d)

D

60.

A fair dice is rolled twice consecutively. If this experiment is carried out 250 times, how many times will at least one perfect square be obtained?

a)

138 times

b)

129 times

c)

130 times

d)

141 times

61.

The probability of appointing Adam as the chairman of the Finance Club (F) and the head of the sports house (S) are $\frac{3}{5}$ and $\frac{2}{9}$ respectively. Calculate the probability of not appointing Adam as the chairman of the Finance Club (F) or the head of the sports house (S)

a)

$\frac{37}{72}$

b)

$\frac{5}{36}$

c)

$\frac{7}{24}$

d)

$\frac{35}{72}$

62.

Eight cards labelled with the letters "T,H,U,R,S,D,A,Y" are put in a box. A card is chosen at random from the box. Calculate the probability that the card chosen is labelled with a vowel or letter "R".

a)

$\frac{3}{4}$

b)

$\frac{5}{8}$

c)

$\frac{1}{4}$

d)

$\frac{3}{8}$

63.

What is the sample spaces for the combined event below:

Two books are chosen at random from a bookshelf that contains a history book (H), two mathematics books (M) and a geography book (G)

a)

{(H,M1),(H,M2),(H,G),(M1,M2),(M1,G),(M2,G)}

b)

(H,M1),(H,M2),(H,G),(M1,H),(M1,M2),(M1,G),(M2,H),(M2,M1),(M2,G),(G,H),(G,M1),(G,M2)

c)

{(H,M1),(H,M2),(H,G),(M1,H),(M1,M2),(M1,G),(M2,H),(M2,M1),(M2,G),(G,H),(G,M1),(G,M2)}

d)

(H,M1),(H,M2),(H,G),(M1,M2),(M1,G),(M2,G)

64.

A study is carried out on the gender of the children from 16 000 families with two children. Estimate the number of families with at least one son in that study.

a)

4 000

b)

8 000

c)

12 000

d)

15 000

65.

Box R contains five red marbles and seven green marbles while Box T contains four red marbles and eight green marbles.

A marble is randomly selected from Box R. If the marble is red, that marble will be put into box T. If the marble is green, that marble will be returned to Box R.

Then, a marble will be randomly selected from Box T. The colors of the selected marble will be recorded.

Calculate the probability of selecting two red marbles.

a)

$\frac{20}{156}$

b)

$\frac{25}{156}$

c)

$\frac{131}{156}$

d)

$\frac{136}{156}$

66.

A study is carried out on the gender of the children from 16 000 families with two children. Estimate the number of families with at least one son in that study.

a)

4 000

b)

8 000

c)

12 000

d)

15 000

67.

Box R contains five red marbles and seven green marbles while Box T contains four red marbles and eight green marbles.

A marble is randomly selected from Box R. If the marble is red, that marble will be put into box T. If the marble is green, that marble will be returned to Box R.

Then, a marble will be randomly selected from Box T. The colors of the selected marble will be recorded.

Calculate the probability of selecting two marbles of different colors.

a)

$\frac{300}{468}$

b)

$\frac{257}{468}$

c)

$\frac{211}{468}$

d)

$\frac{168}{468}$

68.

Pia has eight shirts and three of them are blue shirts. 40% of the shirts that Yana has are blue. $\frac{1}{5}$ of the shirts that Mei Mei has are blue. Pia, Yana and Mei Mei each chooses a shirt at random to attend ad meeting. Calculate the probability that two of them wear blue shirts.

a)

$\frac{139}{200}$

b)

$\frac{43}{200}$

c)

$\frac{61}{200}$

d)

$\frac{157}{200}$

69.

Among 1 000 families living in Taman Bunga Raya, 800 families own a car while 500 families own a motorcycle. There are no family without a car or a motorcycle. A family is selected randomly. Calculate the probability of getting a family that owns a car and a motorcycle.

a)

$\frac{13}{10}$

b)

$\frac{1}{2}$

c)

$\frac{4}{5}$

d)

$\frac{3}{10}$

70.

A box contains 8 apples, 6 oranges, and 4 pears. A fruit is chosen at random from the box. Calculate the probability of choosing

(b) an orange or a pear

a)

$\frac{1}{3}$

b)

$\frac{2}{9}$

c)

$\frac{5}{9}$

d)

$\frac{2}{27}$

71.

A box contains 8 apples, 6 oranges, and 4 pears. A fruit is chosen at random from the box. Calculate the probability of choosing

(a) an apple or a pear

a)

$\frac{8}{18}$

b)

$\frac{4}{18}$

c)

$\frac{2}{3}$

d)

$\frac{6}{18}$

72.

Determine whether the combined events below mutually exclusive events or non-mutually exclusive events.

Shukur turns his head to the left and to the right at the same time.

a)

mutually exclusive

b)

non-mutually exclusive

73.

Determine whether the combined events below mutually exclusive events or non-mutually exclusive events.

Nancy is riding a bicycle, jogging and doing yoga at the same time.

a)

mutually exclusive

b)

non-mutually exclusive

74.

Two events that cannot happen both at the same time?

a)

independent events

b)

mutually exclusive events

c)

dependent events

d)

non-mutually exclusive events

75.

Which of the following are non-mutually exclusive events?

a)

Throwing the ball up and down

b)

Getting both head and a tail when tossing a coin

c)

Going inside and outside of the classroom

d)

Getting a king and a diamond when picking a card from standard deck

76.

Which of the following pairs of events is mutually exclusive?

a)

Cards: Aces and Spades

b)

Two dice: Odd and even

c)

Sit down and stand up

d)

Sit down and scratch your nose

77.

According to an investigation, the probability of rainfall on Mountain X in May is 0.45.

Calculate the probability that Mountain X will have two consecutive rainy days in May.

a)

0.90

b)

0.55

c)

0.3025

d)

0.2025

78.

Cindy flips a coin once, records the result, then flips it again. Does this situation represent INDEPENDENT or DEPENDENT events?

a)

Independent

b)

Dependent

79.

Tom will randomly select from a treat bag containing 6 lollipops and 4 gum balls. Tom will select a treat, replace it, and then select a second treat.

a)

Independent

b)

Dependent

80.

Is the event INDEPENDENT or DEPENDENT?

The spinner is spun twice. What is the probability that it lands on red first and then blue?

a)

Independent

b)

Dependent

Probability of Combined Events

Total questions: 80

Worksheet time: 7hrs 40mins

Similar Resources on Wayground