6
Q:

In a single throw of two dice , find the probability that neither a doublet nor a total of 8 will appear.

 A) 7/15 B) 5/18 C) 13/18 D) 3/16

Explanation:

n(S) = 36

A = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}

B = { (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) }

$\inline n(A)= 6, n(B)=5, n(A\cap B)= 1$

$\inline \therefore$ Required probability = $\inline P(A\cup B)$

= $\inline P(A)+P(B)-P(A\cap B)$

=  $\inline \frac{6}{36}+\frac{5}{36}-\frac{1}{36}$

$\inline =\frac{10}{36}=\frac{5}{18}$

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

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

4 83
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

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

3 84
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

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.

2 115
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

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

1 92
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