# Probability Quiz Set 014

### Question 1

From a deck of 52 cards two cards are drawn at random. What is the probability that both will be King?

A

\${1/221}\$.

B

\$3/6\$.

C

\$2/221\$.

D

\$6/221\$.

Soln.
Ans: a

Number of ways of drawing 2 cards out of 52 = 52C2 = \$(52 × 51)/2\$ = 1326. There are 4 Kings in all, so 2 can be drawn in 4C2 = \$(4 × 3)/2 = 6\$ ways. The probability is 6/1326 = \${1/221}\$.

### Question 2

A box contains 8 orange, 6 khaki and 2 navy marbles. What is the probability of drawing a marble that is not navy if 2 marbles are drawn out randomly?

A

\${91/120}\$.

B

\$2/16\$.

C

\$92/120\$.

D

\$96/120\$.

Soln.
Ans: a

Total number of marbles is 16. Combinations of 2 marbles that are possible = 16C2 = \${16 × 15}/2\$ = 120. Chances of drawing a non-navy ball are 14C2 = \$(14 × (14 - 1))/2\$ = 91. So probability = 91/120 = \${91/120}\$.

### Question 3

Two fair dice are tossed simultaneously. What is the probability of getting two numbers whose product is odd?

A

1/4.

B

2/3.

C

3/4.

D

4/5.

Soln.
Ans: a

Out of a total of 6 × 6 = 36 outcomes, the favorable ones are: 11, 13, 15, 33, 35, 31, 51, 53, 55. So total favorable are: 9. Probability = 9/36 = 1/4.

### Question 4

A carton consists of 100 hats out of which 72 are good, 6 have minor defects and the remaining have major defects. A hat is taken out at random. What is the probability that it has a major defect?

A

\${11/50}\$.

B

\$6/72\$.

C

\$12/50\$.

D

\$16/50\$.

Soln.
Ans: a

Out of 100 outcomes, the ones that favor a hat with a major defect are 100 - 72 - 6 = 22. So probability = 22/100 = \${11/50}\$.

### Question 5

A carton consists of 100 hats out of which 50 are good, 4 have minor defects and the remaining have major defects. A hat is taken out at random. What is the probability that it has a major defect?

A

\${23/50}\$.

B

\$4/50\$.

C

\$24/50\$.

D

\$28/50\$.

Soln.
Ans: a

Out of 100 outcomes, the ones that favor a hat with a major defect are 100 - 50 - 4 = 46. So probability = 46/100 = \${23/50}\$. 