MCQs

Probability Questions with solutions MCQs

1. Let us assume that a student is chosen from a random sample of 80 students, out of which 30 have opted for Maths, 20 opted for physics and 10 have opted for both Maths and Physics. Find the probability that the student has opted for either Maths or Physics.

A

1/2

B

3/2

C

5/2

D

7/2

Probability Secondary Mathematics
Correct Answer : A
Explanation :

1/2

Correct Answered :

Wrong Answered :

2. Determine the probability of drawing either an ace or a heart from a standard deck of 52 cards:

A

16/52

B

17/52

C

4/52

D

13/52

Probability Accounts Assistant LAHDC
Correct Answer : A
Explanation :

16/52

Correct Answered :

Wrong Answered :

3. Revised probability is also know as:

A

Prior Probability

B

Posterior probability

C

Joint probability

D

None of the above

Probability Accounts Assistant LAHDC
Correct Answer : B
Explanation :

A posterior probability, in Bayesian statistics, is the revised or updated probability of an event occurring after taking into consideration new information. The posterior probability is calculated by updating the prior probability using Baye`s theorem.

Correct Answered :

Wrong Answered :

4. What is the probability of at least two heads on three tosses of a fair coin:

A

0.125

B

0.5

C

1

D

0.25

Probability Accounts Assistant LAHDC VERIFIED
Correct Answer : B
Explanation :

Sample space: {HHH, HTH,THH,TTH, HHT, HTT,THT,TTT​}

Total number of possible outcomes=8

Probability of getting at least two heads is:

P(A)=P(getting two heads)+P(getting 3 heads)

= 3/8 + 1/8

= 4/8 = 1/2 = 0.5

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Wrong Answered :

5. A single letter is selected at random from the word RELATION. What is the probability that it is a vowel?

A

4/9

B

3/7

C

1/2

D

1/3

Probability JSA 2021
Correct Answer : C
Explanation :

4/8 = 1/2

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Wrong Answered :

6. X and Y are independent events such that P (Y) = 0.3 and P (X∪Y) = 0.6, then what is the value of P (X)?

A

2/7

B

1/3

C

1/6

D

3/7

Probability JSA 2021
Correct Answer : D
Explanation :

P(X U Y)  = P(X) + P(Y) - P(X ∩ Y).

Since X and Y are independent events therefore

P(X ∩ Y) = P(X) x P(Y).

0.6 = P(X) + 0.3 - P(X) x 0.3

0.6 = 0.7 P(X) + 0.3

0.3 = 0.7 P(X)

P(X) = 0.3/0.7 

=3/7

Correct Answered :

Wrong Answered :

7. A boy is known to speak truth 2 out of 3 times. He throws a dice and reports that it is a three. What is the probability that it is actually a three?

A

1/7

B

1/5

C

2/7

D

2/5

Probability JSA 2021
Correct Answer : C
Explanation :

Let A be the event boy speaks truth

P(A)=2/3

Let B be the Event dice shows 3

P(B) = 1/6

using Bayes therorem

P(B|A) = (P(B).P(A|B))/( P(B) . P(A|B) + P(~B). P(A|~B) )

= (2/18)/(2/18 + 5/18) =2/7

Correct Answered :

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8. A card is drawn at random from a pack of 52 cards. What is the probability that it is a club?

A

1/4

B

1/13

C

1/52

D

1/2

Probability JSA 2021
Correct Answer : A
Explanation :

1/4

Correct Answered :

Wrong Answered :

9. Four balls are drawn at random from a bag containing 5 white and 4 black balls. What is the probability that 2 black and 2 white balls are drawn?

A

5/21

B

10/21

C

10/19

D

5/7

Probability JSA 2021
Correct Answer : B
Explanation :

10/21

Correct Answered :

Wrong Answered :

10. If five coins are tossed together, then what is the probability of getting at least one head?

A

31/32

B

1/64

C

1/32

D

63/64

Probability JSA 2021
Correct Answer : A
Explanation :

First find the probability that NO heads turn up i.e., five tails.
That would be (1/2)5 = 1/32.
For at least one heads to occur is the complement of all tails. It`s probability is 1 - 1/32 = 31/32

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11. The letters K, L, B, C and A are rearranged to form the word BLACK. What is its probability?

A

1/120

B

1/5

C

1/180

D

1/30

Probability JSA 2021
Correct Answer : A
Explanation :

1/120

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Wrong Answered :

12. X can hit a target 3 times in 4 shots. Y, 2 times in 3 shots and Z, 5 times in 6 shots. What is the probability that none of them will hit the target?

A

1/72

B

5/12

C

5/24

D

1/36

Probability JSA 2021
Correct Answer : A
Explanation :

1/72

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Wrong Answered :

13. A fair coin is tossed repeatedly. If tail appears on the first three tosses, then what is the probability of appearance of tail on the fourth toss?

A

1/5

B

1/2

C

1/6

D

1/3

Probability JSA 2021
Correct Answer : B
Explanation :

1/2

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Wrong Answered :

14. Two cards are drawn from a well shuffled pack of 52 cards without replacement. What is the probability that one card is a club and other card is a king of red colour?

A

1/26

B

1/52

C

2/51

D

1/102

Probability JSA 2021
Correct Answer : D
Explanation :

There are total 13 cards of club, so probability that one card is spade is 13/52
According to the questions cards are drawn without replacement. So only 51 cards are left.
Again there are 26 red cards and only two among them are kings
So probability of red king is 2/51
Probability that one card is a club and other card is king of red colour is 13/52 * 2/51 = 1/102

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Wrong Answered :

15. Two dices are thrown together, what is the probability of getting a sum 6?

A

1/9

B

1/6

C

7/36

D

5/36

Probability JSA 2021
Correct Answer : D
Explanation :

Let P(E) be the event of getting sum = 6 .
To get a sum of 6, the possible favorable outcomes are:

(1,5), (2,4), (3,3), (4,2), and (5,1).

Thus, there are 5 favorable outcomes out of 36 hence P(E) = 5/36

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16. If the probability of rain on any given day in Delhi is 1/2, then what is the probability that it rains on exactly 4 days in a six-day period?

A

5/32

B

15/64

C

5/64

D

15/32

Probability JSA 2021
Correct Answer : B
Explanation :

15/64

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Wrong Answered :

17. Three coins are tossed together. What is the probability of getting neither 3 heads nor 2 tails?

A

5/8

B

1/4

C

1/2

D

3/8

Probability JSA 2021 VERIFIED
Correct Answer : C
Explanation :

1/2

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Wrong Answered :

18. In an official party there are 568 glasses of cold drinks at the party, 142 of which contains a lemon flavoured drink. What is the probability that a randomly selected drink will not be lemon flavoured?

A

3/5

B

4/5

C

1/4

D

3/4

Probability Assistant Compiler 2021
Correct Answer : D
Explanation :

3/4

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Wrong Answered :

19. Which among the following term is used to denote the percentage of eligible voters who cast their votes in an election?

A

Turnout

B

Rigging

C

Booth Capturing

D

Level Playing field

Probability Assistant Compiler 2021
Correct Answer : A
Explanation :

Turnout

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Wrong Answered :

20. Suppose you randomly choose a number from 171 to 200, both inclusive. What is the probability that you chose a number which is multiple of 3?

A

1/3

B

3/5

C

2/5

D

2/3

Probability Assistant Compiler 2021
Correct Answer : A
Explanation :

1/3

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Wrong Answered :

21. A basket contains 84 brown shoes and 126 black shoes. A shoe is picked up at random. Find the probability of getting a brown shoe.

A

0.6

B

0.3

C

0.5

D

0.4

Probability Assistant Compiler/Caretaker
Correct Answer : D
Explanation :

0.4

Correct Answered :

Wrong Answered :

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