Free Printable Group 1 - Probability and Counting Techniques

1.

$Simplify\ 14!\cdot\frac{5!}{15!}$

a)

5

b)

7

c)

8

d)

9

2.

$Find\ the\ value\ of\ x\ where\ \frac{3\left(5-x\right)!}{2x}=\left(4-x\right)!$

a)

2

b)

3

c)

5

d)

7

3.

In Cora’s punnet, there are 6 mangoes, 7 lemons, and 8 strawberries. If a fruit is selected randomly, what is the probability that she will select a strawberry or a mango?

a)

$\frac{2}{3}$

b)

$\frac{2}{7}$

c)

$\frac{3}{7}$

d)

$\frac{3}{8}$

4.

In a lottery draw, numbers 1 to 30 are placed on a lottery ball and placed in a lottery machine. If one ball is drawn at random, what is the probability that the number is a multiple of 2 or a multiple of 3?

a)

$\frac{2}{3}$

b)

$\frac{1}{2}$

c)

$\frac{1}{6}$

d)

$\frac{1}{3}$

5.

A coin and a 6-sided dice are to be tossed and rolled at the same time. What is the probability of getting a head and an even number

a)

$\frac{1}{4}$

b)

$\frac{1}{3}$

c)

$\frac{1}{6}$

d)

$\frac{1}{2}$

6.

A 6-colored-roulette is comprised of red, orange, yellow, green, blue, and violet. If it was spun twice, what is the probability of blue being picked both times?

a)

$\frac{1}{30}$

b)

$\frac{1}{36}$

c)

$\frac{1}{42}$

d)

$\frac{1}{48}$

7.

Suppose 4 people check in their hats at a restaurant and they are given back their hats. Find the number of ways such that no person receives his/her own hat.

a)

12

b)

6

c)

9

d)

15

8.

Five people, including Hutao and Qiqi, are to be seated in a row. Qiqi hates Hutao very much. Qiqi wants to be at least two seats away from Hutao. How many ways can these five people be seated if they follow what Qiqi wants?

a)

32

b)

24

c)

12

d)

36

9.

Lisa plans to visit Mona’s house located at the opposite side of town as shown in the map. She always walks south or east direction. In how many routes can Lisa go from her house to Mona’s house?

a)

21

b)

42

c)

63

d)

84

10.

Six people, including Xiao, Yanfei, and Zhongli, are to be seated in a round table. How many different ways can they be seated if Xiao, Yanfei, and Zhongli are one seat apart from each other?

a)

4

b)

8

c)

12

d)

16

11.

A 10-question quiz has 6 true/false questions followed by 4 multiple choice questions. For each multiple-choice question there are four possible answers. In how many different ways is it possible to answer the 10 questions given that 4 of the true or false questions is answered incorrectly and 3 of the multiple-choice questions are answered correctly?

a)

45 ways

b)

75 ways

c)

60 ways

d)

50 ways

12.

A box contains black chips and white chips. A person selects two chips without replacement. If the probability of selecting a black chip and a white chip is $\frac{15}{56}$ , and the probability of selecting a black chip on the first draw is $\frac{3}{8}$ , find the probability of selecting the white chip on the second draw, given that the first chip selected was a black chip.

a)

$\frac{3}{7}$

b)

$\frac{3}{8}$

c)

$\frac{5}{8}$

d)

$\frac{5}{7}$

13.

A box contains 5 yellow marbles, 7 blue marbles and 3 green marbles. Three marbles are taken out from the box at random and are not replaced. What is the probability that the marbles taken out will be one of each color?

a)

$\frac{1}{13}$

b)

$\frac{1}{26}$

c)

$\frac{4}{15}$

d)

$\frac{3}{13}$

14.

A dice is rolled three times. What is the probability that an even number is rolled directly after an odd number?

a)

$\frac{1}{4}$

b)

$\frac{1}{3}$

c)

$\frac{1}{2}$

d)

$\frac{1}{8}$

15.

In how many ways can you distribute 8 identical candies to 4 kids if each of them gets at least one candy?

a)

35

b)

28

c)

30

d)

33

Group 1 - Probability and Counting Techniques

Total questions: 15

Worksheet time: 1hrs 15mins

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