Probability - Aptitude MCQ Questions and Solutions with Explanations

91

In hypergeometric distribution, the trials are

A) Dependent B) Independent C) Collectively Exhaustive D) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

Dependent

92

For a random variable X, E(X) is

A) Harmonic Mean (HM) B) Geometric Mean (GM) C) Arithmetic Mean (AM) D) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

Arithmetic Mean (AM)

93

Probability distribution of a random variable is also known as

A) Probability B) Probability Function C) Distribution Function D) Probability Distribution

Discuss

Answer & Solution

Answer: Option B

Solution:

Probability Function

94

There are 20 balls in a bag which are numbered 1, 2, 3 . . . . . 20. Find the probability that the number marked on the ball taken out of the bag is divisible by 3 or 5.

A) $$\frac{1}{{10}}$$ B) $$\frac{9}{{20}}$$ C) $$\frac{2}{5}$$ D) $$\frac{1}{2}$$

Discuss

Answer & Solution

Answer: Option B

Solution:

Number divisible by 3 = 6
Number divisible by 5 = 4
Number divisible by 3 or 5 = 1
Total number = 6 + 4 - 1 = 9
Probability = $$\frac{9}{{20}}$$

95

What is the probability that a two digit number is not a prime number when a number is chosen at random?

A) $$\frac{7}{{30}}$$ B) $$\frac{{23}}{{30}}$$ C) $$\frac{{21}}{{90}}$$ D) $$\frac{{67}}{{90}}$$

Discuss

Answer & Solution

Answer: Option B

Solution:

Two digit number = 10 . . . . . 99 = 90 number
Prime number between 1 to 100 = 25
Prime number between 1 to 10 = 2, 3, 5, 7 = 4
Prime number between 1 to 99 = 25 - 4 = 21
$${\text{Probability}} = \frac{{90 - 21}}{{90}} = \frac{{69}}{{90}} = \frac{{23}}{{30}}$$

96

A letter of English alphabet is chosen at random, Probability of getting a vowel is-

A) $$\frac{5}{{26}}$$ B) $$\frac{5}{{21}}$$ C) $$\frac{1}{4}$$ D) $$\frac{6}{{25}}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

$${\text{P}}\left( {\text{V}} \right) = \frac{5}{{26}}$$

97

When a coined is tossed once, what are the probability of coming Head?

A) 1 B) $$\frac{1}{2}$$ C) 2 D) 0

Discuss

Answer & Solution

Answer: Option B

Solution:

$${\text{P}} = \frac{1}{2}$$

98

What will be the probability to remove face card from card deck?

A) $$\frac{6}{{13}}$$ B) $$\frac{{12}}{{13}}$$ C) $$\frac{3}{{13}}$$ D) $$\frac{3}{{26}}$$

Discuss

Answer & Solution

Answer: Option C

Solution:

Total card = 52
Face card = 12
$${\text{P}} = \frac{{12}}{{52}} = \frac{3}{{13}}$$

99

A bag contains cards numbered between 33 and 92. If one card is drawn from the bag, the probability of the number of the drawn card is a perfect square is-

A) $$ - \frac{1}{{12}}$$ B) $$\frac{5}{{39}}$$ C) $$\frac{1}{{15}}$$ D) $$\frac{4}{{59}}$$

Discuss

Answer & Solution

Answer: Option D

Solution:

Perfect square between 33 to 92 = 36, 49, 64, 81
Total number = 92 - 33 = 59
$${\text{P}} = \frac{4}{{59}}$$

100

When a pair of dice is thrown, what is the probability of the sum of numbers being odd?

A) 1 B) 0.25 C) 0.4 D) 0.5

Discuss

Answer & Solution

Answer: Option D

Solution:

Total events = 6² = 36
Sum odd = 1, 3, 5, 7, 9, 11
3 = (1, 2)(2, 1)
5 = (1, 4)(4, 1)(2, 3)(3, 2)
7 = (1, 6)(6, 1)(2, 5)(5, 2)(3, 4)(4, 3)
9 = (3, 6)(6, 3)(4, 5)(5, 4)
11 = (6, 5)(5, 6)
$${\text{Probability}} = \frac{{18}}{{36}} = \frac{1}{2} = 0.5$$