## Probability – Aptitude Questions and Answers

Probability aptitude questions and answers section with explanation. Practice online test for various interview, competitive and entrance exams.

1. The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?

A.18/35        B.12/35        C.17/35        D.19/35        E.None of these

Answer: A

Explanation:

If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35

2. Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is -.

A.10/17        B.10/19        C.46/105    D.11/15        E.Cannot be determined

Answer: E

Explanation:

There is no definite formula for finding prime numbers among 15 consecutive numbers. Hence the probability cannot be determined.

3. What is the probability that a leap year has 53 Sundays and 52 Mondays?

A.0        B.1/7        C.2/7        D.5/7        E.6/7

Answer: B

Explanation:

A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7

4. 10 books are placed at random in a shelf. The probability that a pair of books will always be together is -.

A.1/10        B.9/10        C.1/5        D.3/10        E.1/2

Answer: C

Explanation:

10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5

5. Three 6 faced dice are thrown together. The probability that all the three show the same number on them is -.

A.1/216        B.1/36        C.5/9        D.5/12        E.7/12

Answer: B

Explanation:

It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36

6. Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is -.

A.7/12        B.5/9        C.1/36        D.5/12        E.8/9

Answer: B

Explanation:

No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.

7. Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is -.

A.5/9        B.5/12        C.1/36        D.7/12        E.4/9

Answer: B

Explanation:

Using question number 11 and 12, we get the probability as
1 – (1/36 + 5/9) = 5/12

8. A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.

A.6/63        B.2/63        C.125/126    D.1/126        E.1/63

Answer: C

Explanation:

Required probability = 1 – 1/126 = 125/126

9. If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is -.

A.19/52        B.17/52        C.5/13        D.4/13        E.9/26

Answer: D

Explanation:

P(SᴜK) = P(S) + P(K) – P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 – 1/52 = 4/13

10. If six persons sit in a row, then the probability that three particular persons are always together is -.

A.1/20        B.3/10        C.1/5        D.4/5        E.2/5

Answer: C

Explanation:

Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5

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