# Probability Quiz Set 009

### Question 1

64 defective pens are accidentally mixed with 40 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

\${8/13}\$.

B

\$66/104\$.

C

\$9/104\$.

D

\$13/104\$.

Soln.
Ans: a

Out of the total number of pens = 104, the chances favoring defective pen are 64. So the probability is 64/104 = \${8/13}\$.

### Question 2

A piggy bank contains 88 nos. of 50-paise coins, 37 nos. of 1-rupee coins and 34 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

\${88/159}\$.

B

\$34/159\$.

C

\$89/159\$.

D

\$93/159\$.

Soln.
Ans: a

Out of the total number of coins = 159, the chances favoring 50-paise coin are 88. So the probability is 88/159 = \${88/159}\$.

### Question 3

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}\$.

### Question 4

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

A

\${1/221}\$.

B

\$9/12\$.

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 Aces in all, so 2 can be drawn in 4C2 = \$(4 × 3)/2 = 6\$ ways. The probability is 6/1326 = \${1/221}\$.

### Question 5

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

\$3/9\$.

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. 