Probability Quiz Set 005

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

From a deck of 52 cards 1 card is drawn at random. What is the probability that it will be a red "5"?

A

\${1/26}\$.

B

\$5/7\$.

C

\$2/26\$.

D

\$6/26\$.

Soln.
Ans: a

Number of ways of drawing 1 card = 52. There are two red "5" in the whole pack. So favorable chances are 2. Probability = 2/52 = 1/26.

Question 3

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.

Question 4

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

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

Question 5

A piggy bank contains 73 nos. of 50-paise coins, 37 nos. of 1-rupee coins and 81 nos. of 2-rupee coins. The piggy bank is turned upside down, and one coin falls down. What is the probability that it is a 50-paise coin?

A

\${73/191}\$.

B

\$81/191\$.

C

\$74/191\$.

D

\$78/191\$.

Soln.
Ans: a

Out of the total number of coins = 191, the chances favoring 50-paise coin are 73. So the probability is 73/191 = \${73/191}\$.