Probability - Aptitude MCQ Questions and Solutions with Explanations

1

King and Queen of black colour are taken out from a deck of 52 playing cards. A card is drawn from the remaining well-shuffled cards. Probability of getting a spade card is-

A) $$\frac{{11}}{{13}}$$ B) $$\frac{{11}}{{48}}$$ C) $$\frac{{11}}{{52}}$$ D) $$\frac{1}{4}$$

Discuss

Answer & Solution

Answer: Option B

Solution:

Remaining card = 52 - (2)
Black king - 2 (Black queen) = 48
Spade card is black hence 1 queen and 1 king of spade is removed, remaining spade card = 13 - 1 - 1 = 11
Probability = $$\frac{{11}}{{48}}$$

2

One black, one red and one green dice are thrown together, what is the probability of sum of three numbers is ≥ 17.

A) $$\frac{7}{{216}}$$ B) $$\frac{5}{{216}}$$ C) $$\frac{1}{{54}}$$ D) $$\frac{1}{{36}}$$

Discuss

Answer & Solution

Answer: Option C

Solution:

Total events = 6³ = 216
Sum greater than 17 = (6, 6, 6)
Sum equal to 17 = (6, 6, 5)(6, 5, 6)(5, 6, 6)
Probability = $$\frac{4}{{216}}$$ = $$\frac{1}{{54}}$$

3

If tossing three coins at a time, the probability of getting at least one heads is:

A) $$\frac{1}{2}$$ B) $$\frac{1}{8}$$ C) $$\frac{3}{8}$$ D) $$\frac{7}{8}$$

Discuss

Answer & Solution

Answer: Option D

Solution:

At least one head come at least one time, it come also there will be only event in which all three will tale, in which even 1 will not head otherwise less in each at least one head come.
Probability = $$\frac{7}{8}$$

4

A dice is cast twice, and the sum of the appearing numbers is 10. The probability that the number 5 has appeared at least once is-

A) $$\frac{2}{3}$$ B) $$\frac{1}{4}$$ C) $$\frac{1}{2}$$ D) $$\frac{1}{3}$$

Discuss

Answer & Solution

Answer: Option D

Solution:

Total event when sum is 10 = (5, 5)(6, 4)(4, 6)
When 5 occurs = (5, 5)
Probability = $$\frac{1}{3}$$

5

To drawn an ace out the deck of cards probability can be.

A) $$\frac{{12}}{{13}}$$ B) $$\frac{{15}}{{26}}$$ C) $$\frac{9}{{13}}$$ D) $$\frac{1}{{13}}$$

Discuss

Answer & Solution

Answer: Option D

Solution:

Total Ace = 4
Probability = $$\frac{4}{{52}}$$ = $$\frac{1}{{13}}$$

6

There are 30 balls in a bag on which the number 1, 2, 3 . . . . . . . 30 are marked one ball is drawn randomly from the bag. Find the probability that the number marked on the ball taken out of the bag is divisible by 4 or 6.

A) $$\frac{1}{{15}}$$ B) $$\frac{2}{5}$$ C) $$\frac{3}{{10}}$$ D) $$\frac{1}{3}$$

Discuss

Answer & Solution

Answer: Option D

Solution:

Number of divisible by 4 = 7
Number of divisible by 6 = 5
Number of divisible by (4, 5, 6) = 2
Total number = 7 + 5 - 2 = 10
Probability = $$\frac{{10}}{{30}}$$ = $$\frac{1}{3}$$

7

Find, the probability that if a dice is thrown twice, the sum of the digits is 10.

A) $$3$$ B) $$\frac{1}{{36}}$$ C) $$\frac{1}{{12}}$$ D) $$\frac{5}{{36}}$$

Discuss

Answer & Solution

Answer: Option C

Solution:

Total events = 6² = 36
Sum as 10 = (6, 4)(4, 6)(5, 5)
Probability = $$\frac{3}{{36}}$$ = $$\frac{1}{{12}}$$

8

A box contains 6 white, 2 black and 3 red balls. If a ball is drawn at random, what is the probability that it will not be white?

A) $$\frac{5}{{11}}$$ B) $$\frac{6}{{11}}$$ C) $$\frac{5}{9}$$ D) $$\frac{6}{5}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

Total balls ⇒ 6 + 2 + 3 = 11 balls
$$\eqalign{ & P\left( W \right) = \frac{6}{{11}} \cr & P\left( {{\text{not white ball}}} \right) = 1 - \frac{6}{{11}} = \frac{5}{{11}} \cr} $$

9

A box contains 100 pens. Out of which eight are defective. One pen is out from the box. Find the probability that the pen is not defective.

A) $$\frac{{23}}{{25}}$$ B) $$\frac{8}{{10}}$$ C) $$\frac{{100}}{8}$$ D) $$\frac{{25}}{{23}}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

Good pen = 100 - 8 = 92
Probability = $$\frac{{92}}{{100}}$$ = $$\frac{{23}}{{25}}$$