# Probability Quiz Set 016

### Question 1

A box contains 41 red balls and an unknown number of blue balls. If the probability of drawing a blue ball is 3 times the probability of drawing a red ball, then how many blue balls are there in the box?

A

123.

B

128.

C

118.

D

133.

Soln.
Ans: a

Let the number of blue balls be x. Chances of drawing a blue ball are \$x/{x + 41}\$ = 3 × \$41/{x + 41}\$, which gives x = 3 × 41 = 123.

### Question 2

A bag contains 2 Red, 6 Blue and 3 Green marbles. What is the probability of drawing a Red marble if 2 marbles are drawn out randomly?

A

\${19/55}\$.

B

\$3/11\$.

C

\$20/55\$.

D

\$24/55\$.

Soln.
Ans: a

Total number of marbles is 11. Combinations of 2 marbles that are possible = 11C2 = \${11 × 10}/2\$ = 55. If one of the two balls is red, then red + red is one possibility, and 2 × (6 + 3) are the other possibilities. So total favorable outcomes = 1 + 2 × 9 = 19, and the probability is 19/55 = \${19/55}\$.

### Question 3

12 bowls are lying inverted on a table. 8 of them contain marbles, but 4 of them are empty. What is the probability of getting a marble if one of the bowls is opened randomly?

A

\${2/3}\$.

B

\$9/12\$.

C

\$4/3\$.

D

\$7/3\$.

Soln.
Ans: a

Chances favoring a marble are 8, whereas the total chances are 12. The probability is 8/12 = \${2/3}\$.

### Question 4

Karmjeet and Sham are friends. What is the probability that both will have different birthdays, ignoring a leap year?

A

\${364/365}\$.

B

\$21/365\$.

C

\$365/365\$.

D

\$369/365\$.

Soln.
Ans: a

The birthday of second friend has 365 outcomes. If it is not to match the birthday of the first friend, the number of favorable outcomes is 365 - 1 = 364. So probability is 364/365.

### Question 5

Two players, A and B, play a game. It is known that probability of A's victory is 0.58. What is the probability of B's victory?

A

0.42.

B

0.58.

C

0.5.

D

0.25.

Soln.
Ans: a

One of the two is going to win. Probability of A's defeat is 1 - 0.58 = 0.42, which is the probability of B's victory. 