This is aptitude questions and answers section on Probability with explanation for various interview, competitive examinations and entrance tests.

1. The probability that a number selected at random from the first 50 natural numbers is a composite number is -.
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Answer: Option B

Explanation:

The number of exhaustive events = ⁵⁰C₁ = 50.

We have 15 primes from 1 to 50.

Number of favourable cases are 34.

Required probability = 34/50 = 17/25.

2. A coin is tossed live times. What is the probability that there is at the least one tail?
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Answer: Option A

Explanation:

Let P(T) be the probability of getting least one tail when the coin is tossed five times.

= There is not even a single tail.

i.e. all the outcomes are heads.

= 1/32 ; P(T) = 1 - 1/32 = 31/32

3. If a number is chosen at random from the set {1, 2, 3, ...., 100}, then the probability that the chosen number is a perfect cube is -.
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Answer: Option A

Explanation:

We have 1, 8, 27 and 64 as perfect cubes from 1 to 100.

Thus, the probability of picking a perfect cube is

4/100 = 1/25.

4. Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.
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Answer: Option D

Explanation:

n(S) = 20

n(Even no) = 10 = n(E)

n(Prime no) = 8 = n(P)

P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20

5. If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is -.
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Answer: Option B

Explanation:

The number of exhaustive outcomes is 36.

Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2

P(E) = 1 - 1/2 = 1/2.

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