50
Q:

A letter iws takenout at random from 'ASSISTANT'  and another is taken out from 'STATISTICS'. The probability that they are the same letter is :

A) 35/96 B) 19/90
C) 19/96 D) None of these

Answer:   B) 19/90

Explanation:

Here N and C are not common and same letters can be A, I, S, T. Therefore

Probability of choosing A =   = 1/45

Probability of choosing I =  = 1/45

Probability of choosing S =  = 1/10

Probability of choosing T =  = 1/15

Hence, Required probability = 

Q:

What is the probability that a leap year has 53 Saturdays and 52 Sundays ?

A) 1/7 B) 2/7
C) 1/2 D) 3/2
 
Answer & Explanation Answer: A) 1/7

Explanation:

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

Required Probability = 1/7

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3 76
Q:

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  ?

A) 16/19 B) 1
C) 3/2 D) 17/20
 
Answer & Explanation Answer: D) 17/20

Explanation:

n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(E U P) = 10/20 + 8/20 - 1/20 = 17/20

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2 79
Q:

The probability that a number selected at random from the first 100 natural numbers is a composite number is  ?

A) 3/2 B) 2/3
C) 1/2 D) 34/7
 
Answer & Explanation Answer: A) 3/2

Explanation:

The number of exhaustive events = 100 C₁ = 100.

We have 25 primes from 1 to 100.

Number of favourable cases are 75.

Required probability = 75/50 = 3/2.

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2 109
Q:

In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples ?

A) 6/7 B) 19/21
C) 7/31 D) 5/21
 
Answer & Explanation Answer: D) 5/21

Explanation:

Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ x ⁶C₁)

As remaining person can be any one among three couples left.

Required probability = (⁵C₂ x ⁶C₁)/¹⁰C₅
= (10 x 6)/252 = 5/21

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1 80
Q:

If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is  ?

A) 1 B) 1/2
C) 0 D) 3/5
 
Answer & Explanation Answer: B) 1/2

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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