# Probability Quiz Set 011

### Question 1

75 defective pens are accidentally mixed with 36 good ones. It is not possible to just look at a pen and tell whether it is defective or not. One pen is taken out at random. What is the probability that it is a defective pen?

A

\${25/37}\$.

B

\$77/111\$.

C

\$26/111\$.

D

\$30/111\$.

Soln.
Ans: a

Out of the total number of pens = 111, the chances favoring defective pen are 75. So the probability is 75/111 = \${25/37}\$.

### Question 2

11 bowls are lying inverted on a table. 6 of them contain coins, but 5 of them are empty. What is the probability of getting a coin if one of the bowls is opened randomly?

A

\${6/11}\$.

B

\$7/11\$.

C

\$8/11\$.

D

\$11/11\$.

Soln.
Ans: a

Chances favoring a coin are 6, whereas the total chances are 11. The probability is 6/11 = \${6/11}\$.

### Question 3

Two players, A and B, play a game. It is known that probability of A's victory is 0.39. What is the probability of B's victory?

A

0.61.

B

0.39.

C

0.5.

D

0.25.

Soln.
Ans: a

One of the two is going to win. Probability of A's defeat is 1 - 0.39 = 0.61, which is the probability of B's victory.

### Question 4

Two friends were born on non-leap years. What is the chance that their birthdays do not fall on the same day and month of the 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 5

A box contains 3 maroon, 6 green and 2 khaki marbles. What is the probability of drawing a khaki marble if 2 marbles are drawn out randomly?

A

\${19/55}\$.

B

\$2/11\$.

C

\$20/55\$.

D

\$24/55\$.

Soln.
Ans: a

Total number of marbles is 11. Combinations of 2 marbles that are possible = 11C2 = \${11 × 10}/2\$ = 55. If one of the two balls is khaki, then both balls will be khaki in 2C2 = \${2 × (2 - 1)}/2\$ = 1 ways. The number of ways in which non-khaki can be drawn out are 2 × (3 + 6). So total favorable outcomes = 1 + 2 × 9 = 19, and the probability is 19/55 = \${19/55}\$. 