Probability Exercise Sheet 1

1. If a family has three children, find the sample space and then find the probability that two of

three children are girls.

2. When a single dice is rolled:

a- Find the probability of getting a 9.

b- Find the probability of getting a number less than 7.

c- Find the probability of getting an even number, and the probability of getting an odd

number. What do you conclude?

3. If the probability that a person lives in an industrialized country of the world is 1

5 , find the

probability that a person does not live in an industrialized country.

4. In a sample of 50 people, 21 had type O blood, 22 had type A blood, 5 had type B blood, and 2

had type AB blood. Find the probability that

a- A person has type O blood

b- A person has type A or B blood

c- A person does not have type AB blood

5. Suppose that the experiment to toss a balanced coin three times independently.

Define the following events

A is the event of getting at least one head

B is the event of getting exactly two heads and one tail

C is the event of getting all three coins with the same side

a- Determine the sample space of the experiment List the outcomes of each

of the three events A, B, and C.

b- Find the probability for each of the three events A, B, and C.

c- Find the complement events of A, B, C , and their probabilities

d- Find the outcomes and the probabilities of the following events

𝐴 ∪ 𝐵, 𝐴 ∩ 𝐵, 𝐴 ∪ 𝐵 ∪ 𝐶, 𝐵 ∩ 𝐶, 𝐵 ∪ 𝐶

e- Find the probability of A given B

f- Find the probability of B given A

g- Are the events A and B independent? Why?

6. If we have 𝑃(𝐴) = 0.25, 𝑃(𝐵) = 0.5, 𝑃(𝐴 ∪ 𝐵) = 0.8, Find 𝑃(𝐴 ∩ 𝐵), 𝑃(𝐴\𝐵), 𝑃(𝐵\𝐴)

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Probability Exercise Sheet 2

Exercise

1) which of the following is an experiment?

a) Tossing a coin

b) Rolling a single die

c) Choosing a marble from a jar

d) All of the above

2) What is the probability of choosing a vowel from alphabet?

a) 21/26

b) 5/26

c) 1/21

d) None of the above

3) A number between 1 and 11 chosen at random, what is the

probability of choosing an odd number?

a) 1/11

b) 5/11

c) 6/11

d) None of the above

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4) A glass jar contains 5red, 3blue and 2 green jelly beans. If a jelly bean

is chosen at random from the jar. Then which of the following is an

impossible event?

a) Choosing a red jelly bean

b) Choosing a blue jelly bean

c) Choosing a yellow jelly bean

d) None of the above

5) A spinner has 7 equal sectors numbered I to 7 ,if you spin the

spinner, then which of the following is certain event ?

a) Landing on a number less than 7

b) Landing on a number less than 8

c) Landing on a number greater than 1

d) None of the above

6) If a number is chosen at random from the following list

2,3,30,5,7,11,13,17,20,24, then what is the probability that it is prime?

a) 1/10

b) 7/10

c) 5/10

d ) 9/10

7) The sample space of choosing an odd number between 1 and 11 at

random is………………….

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a) {1, 3, 5, 7, 9, 11}

b) {1, 3, 5, 9, 10, 11}

c) {1, 3, 5, 6, 9, 10}

d) None of the above

8) Choose one letter at random from the word mission, and then the

sample space is ……………

a) { m ,I ,s ,s ,I ,o ,n}

b) { m ,I ,s, o ,n}

c) { m ,I ,o ,s ,s }

d) None of the above

9) The sample space of choosing 1 letter at random from 5 vowels is

………………,

a) { a ,e ,I ,o, u}

b) { v ,o ,w ,e, l}

c) {1, 2 ,3 ,4 ,5}

d) None of the above

10 )If S = {1, 2,3 ,5 ,6 ,8,10,11,12 ,13} ,A={2 , 3 ,5} ,and B={2,3 ,11 ,13

},then

i) A ∩ B =…………..

II) A ∪ B =……………………….

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III) (A ∩ B) ′ =……………………….

IV) 𝐴′ = ⋯………………….

11) A student is chosen at random from a class of 16 girls and 14 boys.

The probability that the student chosen is not a girl is ……….

a) 8/15

b) 7/15

c) 1

d) None of the above

12) A number is chosen at random from the following list 2 ,3, 5 ,7 ,11 ,

13, 17 ,19 ,the probability that it is not prime …………..

a) 1

b) 1/8

c) 0

d) None of the above

13) All of the following are mutually exclusive events when a single 6 –

sided die is rolled except ……….

a) Getting a number less than 4 or getting a number greater than 4

b) Getting a 2 or getting an odd number

c) Getting a 2 or getting an even number

d) None of the above

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14) A day of the week is chosen at random. The probability of choosing

a Monday or Tuesday ……

a) 1/7

b) 2/14

c) 2/7

d) 3/7

15) A number between 1 and 10 is chosen at random .The probability

of getting a 5 or an even number ……………………………….

a) 3/5

b) 1/2

c) 1/5

d) 5/14

16) Spin a spinner numbered 1 to 7, and toss a coin .The probability of

getting an odd number on the spinner and a tail on the coin ……..

a) 3/14

b) 2/7

c) 5/14

d) None of the above

17) A jar contains 6 red balls, 3 green balls, 5 white balls, and 7 yellow

balls. Two balls are chosen from the jar, with replacement.

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i) The probability that both balls are green

a) 6/441

b) 2/49

c) 1/49

d ) 9/442

ii) The probability of getting a red and then a yellow ball is…………

a ) 2/21

b) 3/21

c) 13/63

d) 1/21

18) Four cards are chosen from standard deck of 52 playing cards with

replacement .the probability of getting 4 hearts is ……….

a) 13/52

b) 1/16

c) 1/256

19) Two cards are chosen at random from a deck of 52 cards without

replacement. The probability of getting two kings …………..

a) 4/663

b) 1/221

c) 1/69

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20) On a math test, 5 out of 20 students got in A. If three students are

chosen at random without replacement .The probability that all three

got an A on the test is ……….

a)1/114

b) 25/1368

c) 3/400

21) At a middle school, 18 % of all students play football and basketball,

and 32 % of all students play football .the probability that a student

who plays football also plays basketball

a) 56%

b) 178%

c) 50%

22) A large basketball of fruits contains 3 oranges, 2 apples, and 5

bananas. If a piece of fruit is chosen at random, the probability of

getting orange or banana is ……

a) 4/5

b) 1/2

c) 7/10

23) in a class of 30 students ,there are 17 girls and 13 boys .A total of 5

students made an A grade on their report card , three of which were

girls .if a student is a chosen at random . The probability of getting a

girl or an A student is ……..

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a) 19/30

b) 11/15

c) 17/180

24) Which of these numbers cannot be a probability?

a) -0.000001

b) 0.5

c) 20%

25) Two coins are tossed. The probability that on head only is ……..

a) 1/2

b) 1/4

c) 3/4

26) Two dice are rolled; the probability that the sum is equal 5 is …….

a) 3/9

b) 1/9

c) 7/36

27) A die is thrown once what’s the probability that the score is a factor

of 6

a) 1/6

b) 1/2

9

c) 2/3

28) The question do you smoke? Was asked of 100 people.Ruslet are

shown in the table

yes no total

male 19 41 60

female 12 28 40

total 31 69 100

*what is the probability of randomly selected individual being a male

who smokes?

** What is the probability of randomly selected individual being a

male?

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