# Probability Quiz Set 010

### Question 1

A carton consists of 100 cups out of which 66 are good, 8 have minor defects and the remaining have major defects. A cup is taken out at random. What is the probability that it has a major defect?

A

\${13/50}\$.

B

\$8/66\$.

C

\$14/50\$.

D

\$18/50\$.

Soln.
Ans: a

Out of 100 outcomes, the ones that favor a cup with a major defect are 100 - 66 - 8 = 26. So probability = 26/100 = \${13/50}\$.

### Question 2

A box contains 5 cyan, 3 navy and 7 khaki marbles. What is the probability of drawing a marble that is not khaki if 2 marbles are drawn out randomly?

A

\${4/15}\$.

B

\$7/15\$.

C

\$5/105\$.

D

\$9/105\$.

Soln.
Ans: a

Total number of marbles is 15. Combinations of 2 marbles that are possible = 15C2 = \${15 × 14}/2\$ = 105. Chances of drawing a non-khaki ball are 8C2 = \$(8 × (8 - 1))/2\$ = 28. So probability = 28/105 = \${4/15}\$.

### Question 3

From a deck of 52 cards two cards are drawn at random. What is the probability that both one is a hearts, and the other a clubs?

A

\${13/102}\$.

B

\$7/9\$.

C

\$14/102\$.

D

\$18/102\$.

Soln.
Ans: a

Number of ways of drawing 2 cards out of 52 = 52C2 = \$(52 × 51)/2\$ = 1326. There are 13 hearts and 13 clubs in the deck. So 2 such cards can be drawn in 13 × 13 = 169 ways. The probability = 169/1326 = 13/102.

### Question 4

From a deck of 52 cards two cards are drawn at random. What is the probability that both one is a clubs, and the other a hearts?

A

\${13/102}\$.

B

\$8/9\$.

C

\$14/102\$.

D

\$18/102\$.

Soln.
Ans: a

Number of ways of drawing 2 cards out of 52 = 52C2 = \$(52 × 51)/2\$ = 1326. There are 13 clubs and 13 hearts in the deck. So 2 such cards can be drawn in 13 × 13 = 169 ways. The probability = 169/1326 = 13/102.

### Question 5

From a deck of 52 cards 1 card is drawn at random. What is the probability that it will be a red "10"?

A

\${1/26}\$.

B

\$4/5\$.

C

\$2/26\$.

D

\$6/26\$.

Soln.
Ans: a

Number of ways of drawing 1 card = 52. There are two red "10" in the whole pack. So favorable chances are 2. Probability = 2/52 = 1/26. 