# Probability Quiz Set 019

### Question 1

A carton consists of 100 cones out of which 47 are good, 3 have minor defects and the remaining have major defects. A cone is taken out at random. What is the probability that it has a major defect?

A

\${1/2}\$.

B

\$3/47\$.

C

\$2/2\$.

D

\$6/2\$.

Soln.
Ans: a

Out of 100 outcomes, the ones that favor a cone with a major defect are 100 - 47 - 3 = 50. So probability = 50/100 = \${1/2}\$.

### Question 2

A carton consists of 100 bowls out of which 74 are good, 6 have minor defects and the remaining have major defects. A bowl is taken out at random. What is the probability that it has a major defect?

A

\${1/5}\$.

B

\$6/74\$.

C

\$2/5\$.

D

\$6/5\$.

Soln.
Ans: a

Out of 100 outcomes, the ones that favor a bowl with a major defect are 100 - 74 - 6 = 20. So probability = 20/100 = \${1/5}\$.

### Question 3

From a deck of 52 cards two cards are drawn at random. What is the probability that both will be "8"?

A

\${1/221}\$.

B

\$7/8\$.

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

### Question 4

A box contains 6 sky blue, 3 red and 8 khaki marbles. What is the probability of drawing a khaki marble if 2 marbles are drawn out randomly?

A

\${25/34}\$.

B

\$8/17\$.

C

\$26/136\$.

D

\$30/136\$.

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 khaki, then both balls will be khaki in 8C2 = \${8 × (8 - 1)}/2\$ = 28 ways. The number of ways in which non-khaki can be drawn out are 8 × (6 + 3). So total favorable outcomes = 28 + 8 × 9 = 100, and the probability is 100/136 = \${25/34}\$.

### Question 5

Two fair dice are tossed simultaneously. What is the probability that the total score is a prime number?

A

5/12.

B

3/5.

C

1/6.

D

5/36.

Soln.
Ans: a

Out of a total of 6 × 6 = 36 outcomes, the favorable ones are: (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5). So total favorable are: 15. Probability = 15/36 = 5/12. This Blog Post/Article "Probability Quiz Set 019" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-08