# Probability Quiz Set 004

### Question 1

A dice is thrown once. What is the probability that we get a number greater than 4?

A

1/3.

B

2/3.

C

5/6.

D

1.

Soln.
Ans: a

Total outcomes = 6. Favorable outcomes are 2: getting a 5 or 6. The required probability is 2/6 = 1/3.

### Question 2

A class has 3 boys and 2 girls. What is the probability of choosing 1 boy and 2 girls?

A

\${3/10}\$.

B

\$4/5\$.

C

\$4/10\$.

D

\$8/10\$.

Soln.
Ans: a

Three students have to be picked. Total number of ways = 5C3 = \${5 × 4 × 3}/{3 × 2 × 1} = \$10. Number of ways of picking 1 boy and 2 girls = 3C1 × 2C2 = 3. So probability = \$3/10\$ = \${3/10}\$.

### Question 3

A box contains 6 cyan, 3 pink and 8 orange marbles. What is the probability of drawing a orange 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 orange, then both balls will be orange in 8C2 = \${8 × (8 - 1)}/2\$ = 28 ways. The number of ways in which non-orange 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 4

Three unbiased coins are tossed. What is the probability of getting at most two heads?

A

7/8.

B

3/8.

C

1/8.

D

5/8.

Soln.
Ans: a

Three coins will give 8 possibilities = 2 × 2 × 2. At most two heads means 1 or 2 heads. We will not get this only when all tails come, which is possible only once. So 8 - 1 = 7 chances are favorable. The probability = 7/8.

### Question 5

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}\$.