Quiz about Probability Final Exam

Question 1

If you toss a coin 10 times and get tails each time, which of the following is true?

Accepted Answer

The probability of getting a head on the next toss is $$\frac{1}{2}.$$

Answer

The probability of getting a tail on the next toss is more than $$\frac{1}{2}.$$

Answer

The probability of getting a head on the next toss is more than $$\frac{1}{2}.$$

Answer

The probability of getting a tail on the next toss is greater than the probability of getting a head.

Question 2

What is the sample space for the jar of marbles?

Accepted Answer

red, yellow, green, blue

Answer

red

Answer

red and yellow

Answer

red and green

Question 3

What is the probability of landing on the color blue on the spinner?

Accepted Answer

$$\frac{3}{12}$$

Answer

$$\frac{3}{3}$$

Answer

1

Answer

$$\frac{3}{9}$$

Question 4

A die is rolled once. What is the probability of rolling a 5?

Accepted Answer

$$\frac{1}{6}$$

Answer

$$\frac{1}{3}$$

Answer

$$\frac{2}{5}$$

Answer

$$\frac{5}{6}$$

Question 5

What is the probability of the spinner landing on red?

Accepted Answer

$$\frac{5}{12}$$

Answer

$$\frac{7}{12}$$

Answer

$$\frac{5}{5}$$

Answer

$$\frac{5}{10}$$

Question 6

A bag has 3 red marbles, 2 blue and 4 green and 1 yellow. What is the theoretical probability of pulling a red?

Accepted Answer

$$\frac{3}{10}$$

Answer

$$\frac{3}{9}$$

Answer

$$\frac{1}{10}$$

Answer

$$\frac{1}{9}$$

Question 7

What is the probability of rolling a 3 and spinning a red?

Accepted Answer

$$\frac{1}{24}$$ =.041666

Answer

$$\frac{1}{6}$$ =.16666

Answer

$$\frac{1}{4}$$ =.25

Answer

$$\frac{1}{10}=.1$$

Question 8

What is the probability of flipping the coin and getting heads up, then getting a T from the group of letters.

Accepted Answer

$$\frac{2}{12}$$ =.1666

Answer

$$\frac{6}{12}$$ =.5

Answer

$$\frac{4}{12}$$ =.3333

Answer

$$\frac{3}{12}$$ =.25

Question 9

What is the probability of drawing a blue color and a number 4?

Accepted Answer

$$\frac{4}{60}=.06666$$

Answer

$$\frac{24}{60}$$ =.4

Answer

$$\frac{10}{60}$$ =.16666

Answer

$$\frac{10}{16}=.625$$

Question 10

A regular 6-sided die is to be rolled once. What is the probability that a number less than 3 is rolled?

Accepted Answer

$$\frac{2}{6}$$

Answer

$$\frac{1}{6}$$

Answer

$$\frac{3}{6}$$

Answer

$$\frac{4}{6}$$

Question 11

A regular 6-sided die is to be rolled once. What is the probability that a number less than or equal to 4 is rolled?

Accepted Answer

$$\frac{4}{6}$$

Answer

$$\frac{3}{6}$$

Answer

$$\frac{1}{4}$$

Answer

$$\frac{5}{6}$$

Question 12

A spinner has 8 equal regions. Each region is marked with one of the following numbers: 10, 20, 30, 40, 50, 60, 70, 80. What is the probability of an even number being spun on the first roll?

Accepted Answer

1

Answer

$$\frac{1}{8}$$

Answer

$$\frac{1}{2}$$

Answer

2

Question 13

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement.P(both marbles are purple)

Accepted Answer

$$\frac{20}{90}=.22222$$

Answer

$$\frac{25}{100}=\ .25$$

Answer

$$\frac{10}{20}=.5$$

Answer

$$\frac{20}{100}$$

Question 14

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement. P(1st orange then green)

Accepted Answer

$$\frac{6}{90}=.06666$$

Answer

$$\frac{6}{100}$$ =.06

Answer

$$\frac{5}{10}=.5$$

Answer

$$\frac{5}{100}=.05$$

Question 15

A basket contains four apples and six peaches. You randomly select one piece of fruit and eat it. Then you randomly select another piece of fruit. What is the probability that both pieces of fruit are apples.

Accepted Answer

$$\frac{12}{90}$$ =.1333

Answer

$$\frac{1}{24}$$ =.04166

Answer

$$\frac{16}{100}$$ =.16

Answer

$$\frac{1}{16}$$ =.0625

Question 16

If you select a marble without looking, how likely is it that you will pick a black one?

Accepted Answer

impossible

Answer

certain

Answer

probable

Answer

unlikely

Question 17

A box contains 3 black pens, 7 blue pens, and 5 red pens. Without looking, P(red or black)

Accepted Answer

$$\frac{8}{15}$$

Answer

$$\frac{15}{225}$$

Answer

$$\frac{5}{15}$$

Answer

$$\frac{2}{15}$$

Question 18

You spin this spinner 3 times.
Find the probability of these 3 events.
P(red, odd, 3)

Accepted Answer

$$\frac{3}{216}=.013888$$

Answer

$$\frac{1}{216}=.0046296$$

Answer

$$\frac{5}{18}=.2777$$

Answer

$$\frac{1}{12}=.08333$$

Question 19

The probability of it raining today is .30. What is the probability that it will NOT rain?

Accepted Answer

.70

Answer

.30

Answer

1

Answer

0

Question 20

What is the P( not purple) on this spinner?

Accepted Answer

$$\frac{4}{5}$$

Answer

$$\frac{2}{5}$$

Answer

$$\frac{1}{5}$$

Answer

$$\frac{1}{4}$$

Question 21

When it comes to tossing dice, the probability of getting a certain roll...

Accepted Answer

Is independent of any other rolls

Answer

Depends on what you just rolled before

Answer

Depends on the date

Question 22

A box contains 5 red socks and 7 blue socks. If you pick out two at random without replacement, what is P(2nd sock is blue | 1st sock is blue)?

Accepted Answer

$$\frac{6}{11}$$

Answer

$$\frac{7}{12}$$

Answer

$$\frac{7}{12}\cdot\frac{6}{11}$$

Question 23

A box contains 5 red socks and 7 blue socks. If you pick out two at random without replacement, what is P(both socks are blue)?

Accepted Answer

$$\frac{7}{12}\cdot\frac{6}{11}$$

Answer

$$\frac{6}{11}$$

Answer

$$\frac{7}{12}$$

Question 24

How many ways can I line up 4 of my 8 friends for a picture?

Accepted Answer

$$8\cdot7\cdot6\cdot5$$

Answer

$$8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1$$

Answer

$$8\cdot8\cdot8\cdot8$$

Answer

$$4\cdot3\cdot2\cdot1$$

Question 25

If the probability of winning a game is .6, and the probability of losing the game is .25, what is the probability of a tie?

Accepted Answer

.15

Answer

.25

Answer

.85

Answer

.35

Question 26

Tim is rolling a die. Tim says "P(getting a 6 | I just got a 4) =P( getting a 6)".

Is he correct? Why?

Accepted Answer

He is right because rolls of dice are independent.

Answer

He is wrong because conditional probabilities much take the condition into account.

Answer

He is wrong because you can't get a 6 and a 4 at the same time.

Question 27

Permutation or Combination: Assigning 5 different offices to 5 different people.

Accepted Answer

Permutation

Answer

Combination

Question 28

Permutation or Combination: Assigning 5 employees to attend a company training.

Accepted Answer

Combination

Answer

Permutation

Question 29

10 co-workers went to lunch. 3 had lobster, 5 had shrimp, and 2 had salmon. How many ways could this have occured?

Accepted Answer

10C3 x 7C5 x 2C2

Answer

10C3 x 10C5 x 10C2

Answer

10C3+10C5+10C2

Answer

10C3+7C5+2C2

Question 30

Anthony is dealing cards (without replacement) from a standard deck of cards.

Find P(the 3rd card is red | the first 2 cards were red)

Accepted Answer

$$\frac{24}{50}$$

Answer

$$\frac{26}{52}\cdot\frac{25}{51}\cdot\frac{24}{50}$$

Answer

$$\frac{24}{52}$$

Answer

$$\frac{26}{52}$$

Question 31

What is going on in the tree diagram?

Accepted Answer

A person has 3 choices for sandwich, 2 choices for side and 2 choices for drink.

There are a total of 12 possible outcomes.

Answer

A person has 3 choices for sandwich, 2 choices for side and 2 choices for drink.

There are a total of 7 possible outcomes.

Answer

A person has 3 choices for sandwich, 6 choices for side and 12 choices for drink.

There are a total of 216 possible outcomes.

Question 32

If I have a standard deck of cards, how many ways can I get a hand of 6 cards that is half red and half black?

Accepted Answer

26C3 x 26x3

Answer

52C6

Answer

52C3 x 49C3

Question 33

When would you use P(A)xP(B)

Accepted Answer

When you want the probability of A AND B both occurring and A and B are independent

Answer

When you want the probability of A OR B occurring and A and B are independent

Answer

When you want the probability of A and B both occurring and A and B are dependent

Answer

When you want the probability of A OR B occurring and A and B are dependent

Question 34

When is P(A) = P(A | B) ?

Accepted Answer

When A and B are independent

Answer

When A and B are dependent

Answer

When B is not possible

Question 35

Soren is taking cards out of a standard deck without replacement. How do you calculate the probability that the first 3 cards are kings?

Accepted Answer

$$\frac{4}{52}\cdot\frac{3}{51}\cdot\frac{2}{50}$$

Answer

$$\frac{4}{52}\cdot\frac{4}{52}\cdot\frac{4}{52}$$

Answer

$$\frac{1}{4}\cdot\frac{1}{4}\cdot\frac{1}{4}$$

Answer

$$\frac{1}{4}\cdot\frac{1}{3}\cdot\frac{1}{2}$$

Question 36

Connor is taking cards out of a standard deck, replacing them and shuffling before taking another. How do you calculate the probability that the first 3 cards are kings?

Accepted Answer

$$\frac{4}{52}\cdot\frac{4}{52}\cdot\frac{4}{52}$$

Answer

$$\frac{4}{52}\cdot\frac{3}{51}\cdot\frac{2}{50}$$

Answer

$$\frac{1}{4}\cdot\frac{1}{4}\cdot\frac{1}{4}$$

Answer

$$\frac{1}{4}\cdot\frac{1}{3}\cdot\frac{1}{2}$$

Question 37

Emma is taking cards out of a standard deck without replacement. How do you calculate the probability that the first 5 cards are kings?

Accepted Answer

$$The\ probability\ is\ 0$$

Answer

$$\frac{4}{52}\cdot\frac{3}{51}\cdot\frac{2}{50}\cdot\frac{1}{49}\cdot\frac{1}{49}$$

Answer

$$\frac{4}{52}\cdot\frac{4}{52}\cdot\frac{4}{52}\cdot\frac{4}{52}\cdot\frac{4}{52}$$

Question 38

Brandon is taking cards out of a standard deck,replacing them and shuffling before taking another. How do you calculate the probability that the first 5 cards are kings?

Accepted Answer

$$\frac{4}{52}\cdot\frac{4}{52}\cdot\frac{4}{52}\cdot\frac{4}{52}\cdot\frac{4}{52}$$

Answer

$$\frac{4}{52}\cdot\frac{3}{51}\cdot\frac{2}{50}\cdot\frac{1}{49}\cdot\frac{1}{49}$$

Answer

$$The\ probability\ is\ 0$$

Question 39

What is the value of 5! - 4!

Accepted Answer

96

Answer

1 !

Answer

5

Answer

4

Question 40

Why is rolling a sum of 7 on 2 dice more likely than rolling a 3?

Accepted Answer

There are more ways to add up to 7 with 2 dice than adding to 3

Answer

3 is a smaller number

Answer

Bigger numbers are always more likely

Answer

3 is the least likely sum of two dice

Question 41

If P(A) > P(B), this means...

Accepted Answer

Event A is more likely to occur than event B

Answer

Events A and B are independent

Answer

Events A and B cannot both occur

Answer

Event A is less likely to occur than event B

Probability Final Exam

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