# Probability Quiz Set 005

### Question 1

A box contains 5 maroon, 4 pink and 8 sky blue balls. What is the probability of drawing a ball that is neither pink nor maroon?

A

\${8/17}\$.

B

\$9/17\$.

C

\$9/136\$.

D

\$13/136\$.

Soln.
Ans: a

Total number of marbles is 17. We have to basically find the probability of picking a sky blue ball, for which 8 chances are favorable. So probability = 8/17 = \${8/17}\$.

### Question 2

9 bowls are lying inverted on a table. 2 of them contain prizes, but 7 of them are empty. What is the probability of getting a prize if one of the bowls is opened randomly?

A

\${2/9}\$.

B

\$3/9\$.

C

\$4/9\$.

D

\$7/9\$.

Soln.
Ans: a

Chances favoring a prize are 2, whereas the total chances are 9. The probability is 2/9 = \${2/9}\$.

### Question 3

A bag contains 2 Red, 8 Blue and 7 Green marbles. What is the probability of drawing a Red marble if 2 marbles are drawn out randomly?

A

\${31/136}\$.

B

\$7/17\$.

C

\$32/136\$.

D

\$36/136\$.

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 red, then red + red is one possibility, and 2 × (8 + 7) are the other possibilities. So total favorable outcomes = 1 + 2 × 15 = 31, and the probability is 31/136 = \${31/136}\$.

### Question 4

From a deck of 52 cards two cards are drawn at random. What is the probability that both will be "10"?

A

\${1/221}\$.

B

\$9/15\$.

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

### Question 5

A box contains 3 pink, 4 maroon and 6 orange marbles. What is the probability of drawing a orange marble if 2 marbles are drawn out randomly?

A

\${19/26}\$.

B

\$6/13\$.

C

\$20/78\$.

D

Soln.
Ans: a

Total number of marbles is 13. Combinations of 2 marbles that are possible = 13C2 = \${13 × 12}/2\$ = 78. If one of the two balls is orange, then both balls will be orange in 6C2 = \${6 × (6 - 1)}/2\$ = 15 ways. The number of ways in which non-orange can be drawn out are 6 × (3 + 4). So total favorable outcomes = 15 + 6 × 7 = 57, and the probability is 57/78 = \${19/26}\$. 