# Probability Quiz Set 003

### Question 1

A box contains 8 khaki, 2 sky blue and 7 navy marbles. What is the probability of drawing a navy marble if 2 marbles are drawn out randomly?

A

\${91/136}\$.

B

\$7/17\$.

C

\$92/136\$.

D

\$96/136\$.

Soln.
Ans: a

Total number of marbles is 17. Combinations of 2 marbles that are possible = 17C2 = \${17 × 16}/2\$ = 136. If one of the two balls is navy, then both balls will be navy in 7C2 = \${7 × (7 - 1)}/2\$ = 21 ways. The number of ways in which non-navy can be drawn out are 7 × (8 + 2). So total favorable outcomes = 21 + 7 × 10 = 91, and the probability is 91/136 = \${91/136}\$.

### Question 2

From a deck of 52 cards 1 card is drawn at random. What is the probability that it will be a red "5"?

A

\${1/26}\$.

B

\$5/7\$.

C

\$2/26\$.

D

\$6/26\$.

Soln.
Ans: a

Number of ways of drawing 1 card = 52. There are two red "5" in the whole pack. So favorable chances are 2. Probability = 2/52 = 1/26.

### Question 3

Three unbiased coins are tossed. What is the probability of getting at most two heads?

A

7/8.

B

3/8.

C

1/8.

D

5/8.

Soln.
Ans: a

Three coins will give 8 possibilities = 2 × 2 × 2. At most two heads means 1 or 2 heads. We will not get this only when all tails come, which is possible only once. So 8 - 1 = 7 chances are favorable. The probability = 7/8.

### Question 4

A box contains 3 navy, 4 green and 5 khaki marbles. What is the probability of drawing a marble that is not khaki if 2 marbles are drawn out randomly?

A

\${7/22}\$.

B

\$5/12\$.

C

\$8/66\$.

D

\$12/66\$.

Soln.
Ans: a

Total number of marbles is 12. Combinations of 2 marbles that are possible = 12C2 = \${12 × 11}/2\$ = 66. Chances of drawing a non-khaki ball are 7C2 = \$(7 × (7 - 1))/2\$ = 21. So probability = 21/66 = \${7/22}\$.

### Question 5

What is the probability of getting a sum of 13 from two throws of a dice?

A

0.

B

1/3.

C

2/3.

D

1/6.

Soln.
Ans: a

Total outcomes = 36. Favorable are 0 because maximum sum possible is 6 + 6 = 12. So probability = 0. 