# Probability Quiz Set 008

### Question 1

Karmjeet and Sham are friends. What is the probability that both will have different birthdays, ignoring a leap year?

A

\${364/365}\$.

B

\$21/365\$.

C

\$365/365\$.

D

\$369/365\$.

Soln.
Ans: a

The birthday of second friend has 365 outcomes. If it is not to match the birthday of the first friend, the number of favorable outcomes is 365 - 1 = 364. So probability is 364/365.

### Question 2

One card is drawn at random from a pack of 52 cards. What is the probability that it is NEITHER a Jack, nor a Queen or a King?

A

10/13.

B

5/26.

C

1/13.

D

3/13.

Soln.
Ans: a

There are 12 such face cards in the entire deck of 52 cards, so the required probability of getting one of them is 12/52 = 3/13. The probability of NOT getting is 1 - 3/13 = 10/13.

### Question 3

A bag contains 2 Red, 4 Blue and 8 Green marbles. What is the probability of drawing a Red marble if 2 marbles are drawn out randomly?

A

\${25/91}\$.

B

\$8/14\$.

C

\$26/91\$.

D

\$30/91\$.

Soln.
Ans: a

Total number of marbles is 14. Combinations of 2 marbles that are possible = 14C2 = \${14 × 13}/2\$ = 91. If one of the two balls is red, then red + red is one possibility, and 2 × (4 + 8) are the other possibilities. So total favorable outcomes = 1 + 2 × 12 = 25, and the probability is 25/91 = \${25/91}\$.

### Question 4

If P(E) = 0.54, then what is the probability of non-occurrence of E?

A

0.46.

B

0.54.

C

0.5.

D

0.25.

Soln.
Ans: a

P(E) + P(non-occurrence of E) is always = 1. So P(non-occurrence of E) = 1 - P(E) = 0.46.

### Question 5

A piggy bank contains 31 nos. of 50-paise coins, 66 nos. of 1-rupee coins and 71 nos. of 2-rupee coins. The piggy bank is turned upside down, and one coin falls down. What is the probability that it is a 50-paise coin?

A

\${31/168}\$.

B

\$71/168\$.

C

\$32/168\$.

D

\$36/168\$.

Soln.
Ans: a

Out of the total number of coins = 168, the chances favoring 50-paise coin are 31. So the probability is 31/168 = \${31/168}\$.