Probability Mcqs - Set 3

1)   Three 6 faced dice are thrown together. The probability that all the three show the same number on them is -.

a. 1/216
b. 1/36
c. 5/9
d. 5/12
Answer  Explanation 

ANSWER: 1/36

Explanation:
It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.

Hence the probability is 6/216 = 1/36


2)   A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is__________?

a. 25/42
b. 9/20
c. 10/23
d. 41/42
Answer  Explanation 

ANSWER: 25/42

Explanation:
Total fruits = 9

Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42.


3)   A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -.

a. 8/15
b. 2/5
c. 3/5
d. 7/15
Answer  Explanation 

ANSWER: 7/15

Explanation:
Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.

Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 7/15


4)   If six persons sit in a row, then the probability that three particular persons are always together is____________?

a. 1/20
b. 3/10
c. 1/5
d. 4/5
Answer  Explanation 

ANSWER: 1/5

Explanation:
Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5


5)   If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is__________?

a. 19/52
b. 17/52
c. 5/13
d. 4/13
Answer  Explanation 

ANSWER: 4/13

Explanation:
P(SᴜK) = P(S) + P(K) – P(S∩K), where S denotes spade and K denotes king.

P(SᴜK) = 13/52 + 4/52 – 1/52 = 4/13


6)   If four coins are tossed, the probability of getting two heads and two tails is__________?

a. 3/8
b. 6/11
c. 2/5
d. 4/5
Answer  Explanation 

ANSWER: 3/8

Explanation:
Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.

n(E) = six ways
p(E) = 6/24 = 3/8


7)   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. 1/4
b. 1/2
c. 3/4
d. 3/5
Answer  Explanation 

ANSWER: 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.


8)   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. 1/2
b. 16/19
c. 4/5
d. 17/20
Answer  Explanation 

ANSWER: 17/20

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


9)   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___________?

a. 1/25
b. 1/2
c. 4/13
d. 1/10
Answer  Explanation 

ANSWER: 1/25

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.


10)   A coin is tossed live times. What is the probability that there is at the least one tail?

a. 31/32
b. 1/16
c. 1/2
d. 1/32
Answer  Explanation 

ANSWER: 31/32

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


11)   The probability that a number selected at random from the first 50 natural numbers is a composite number is__________?

a. 21/25
b. 17/25
c. 4/25
d. 8/25
Answer  Explanation 

ANSWER: 17/25

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.