# Probability Quiz Set 001

### Question 1

A bag contains 2 Red, 8 Blue and 4 Green marbles. What is the probability of drawing a Red marble if 2 marbles are drawn out randomly?

A

\${25/91}\$.

B

\$4/14\$.

C

\$26/91\$.

D

\$30/91\$.

Soln.
Ans: a

Total number of marbles is 14. Combinations of 2 marbles that are possible = 14C2 = \${14 × 13}/2\$ = 91. If one of the two balls is red, then red + red is one possibility, and 2 × (8 + 4) are the other possibilities. So total favorable outcomes = 1 + 2 × 12 = 25, and the probability is 25/91 = \${25/91}\$.

### Question 2

A box contains 83 red balls and an unknown number of blue balls. If the probability of drawing a blue ball is 5 times the probability of drawing a red ball, then how many blue balls are there in the box?

A

415.

B

420.

C

410.

D

425.

Soln.
Ans: a

Let the number of blue balls be x. Chances of drawing a blue ball are \$x/{x + 83}\$ = 5 × \$83/{x + 83}\$, which gives x = 5 × 83 = 415.

### Question 3

Two players, A and B, play a game. It is known that probability of A's victory is 0.48. What is the probability of B's victory?

A

0.52.

B

0.48.

C

0.5.

D

0.25.

Soln.
Ans: a

One of the two is going to win. Probability of A's defeat is 1 - 0.48 = 0.52, which is the probability of B's victory.

### Question 4

Two players, A and B, play a game. It is known that probability of A's victory is 0.34. What is the probability of B's victory?

A

0.66.

B

0.34.

C

0.5.

D

0.25.

Soln.
Ans: a

One of the two is going to win. Probability of A's defeat is 1 - 0.34 = 0.66, which is the probability of B's victory.

### Question 5

A box contains 20 red balls and an unknown number of blue balls. If the probability of drawing a blue ball is 5 times the probability of drawing a red ball, then how many blue balls are there in the box?

A

100.

B

105.

C

95.

D

110.

Soln.
Ans: a

Let the number of blue balls be x. Chances of drawing a blue ball are \$x/{x + 20}\$ = 5 × \$20/{x + 20}\$, which gives x = 5 × 20 = 100.