Probability Quiz Set 001

Question 1

45 defective pens are accidentally mixed with 40 good ones. It is not possible to just look at a pen and tell whether it is defective or not. One pen is taken out at random. What is the probability that it is a defective pen?

A

\${9/17}\$.

B

\$47/85\$.

C

\$10/85\$.

D

\$14/85\$.

Soln.
Ans: a

Out of the total number of pens = 85, the chances favoring defective pen are 45. So the probability is 45/85 = \${9/17}\$.

Question 2

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 3

Two fair dice are tossed simultaneously. What is the probability of getting two numbers whose product is odd?

A

1/4.

B

2/3.

C

3/4.

D

4/5.

Soln.
Ans: a

Out of a total of 6 × 6 = 36 outcomes, the favorable ones are: 11, 13, 15, 33, 35, 31, 51, 53, 55. So total favorable are: 9. Probability = 9/36 = 1/4.

Question 4

What is the probability of getting a sum of 7 from two throws of a dice?

A

1/6.

B

1/3.

C

6/7.

D

7/6.

Soln.
Ans: a

Total outcomes = 36. Favorable are 6, which are: (1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3). Probability = 6/36 = 1/6.

Question 5

A box contains 2 navy, 4 red and 6 sky blue marbles. What is the probability of drawing a marble that is not sky blue if 2 marbles are drawn out randomly?

A

\${5/22}\$.

B

\$6/12\$.

C

\$6/66\$.

D

\$10/66\$.

Soln.
Ans: a

Total number of marbles is 12. Combinations of 2 marbles that are possible = 12C2 = \${12 × 11}/2\$ = 66. Chances of drawing a non-sky blue ball are 6C2 = \$(6 × (6 - 1))/2\$ = 15. So probability = 15/66 = \${5/22}\$.