Quant Mania: Probability (with Solution Key)

Dear Readers,

Today we are presenting you Quant Mania on probability which is very important for your upcoming LIC AAO, Syndicate Bank PO, SIDBI Officers Scale Grade A and other exams. You may expect same questions in your upcoming exams. Try to solve it.

Quant Mania: Probability

Directions (1-7): Study the given information carefully and answer the questions that follow—

A basket contains 4 red, 5 blue, and 3 green marbles.

1. If three marbles are picked at random, what is the probability that either all green or all are red?
a) 1/7
b) 1/44
c) 7/44
d) 5/7
e) None of these



2. If two marbles are drawn at random, what is the probability that both are red?
a) 7/66
b) 1/66
c) 1/220
d) 1/11
e) None of these



3. If two marbles are picked at random, what is the probability that none of them blue?
a) 7/22
b) 21/22
c) 21/220
d) 1/22
e) None of these



4. If three marbles are picked at random, what is the probability that at least one is blue?
a) 1/44
b) 1
c) 37/44
d) 1/37
e) None of these



5. If three marbles are picked at random, what is the probability that two of them are blue and one is green?
a) 1/22
b) 2/22
c) 3/22
d) 4/22
e) None of these



6. If four marbles are picked at random, what is the probability that two of them are red and two are green?
a) 2/55
b) 1/55
c) 4/55
d) 1/220
e) None of these



7. If four marbles are picked at random, what is the probability that one is green, two are blue and one is red?
a) 5/33
b) 8/33
c) 7/33
d) 1/33
e) None of these

Solution

1.b

Red = 4, Blue = 5, Green = 3

Total = 4+5+3 = 12

If 3 marbles are picked, then total Probability = ¹²C₃ = 220

Favorable no of cases = ⁴C₃ + ³C₃ = 4 + 1 = 5

Then, Probability = 5/220 = 1/44

2. d

If 2 marbles are picked, then total Probability = ¹²C₂ = 66

Favorable no of cases = ⁴C₂ = 6

Then, Probability = 6/66 = 1/11

3. a

If 2 marbles are picked, then total Probability = ¹²C₂ = 66

Favorable no of cases without blue (4+3 = 7) = ⁷C₂ = 21

Then, Probability = 21/66 = 7/22

4. c

If 3 marbles are picked, then total Probability = ¹²C₃ = 220

Favorable no of cases without blue (4+3 = 7) = ⁷C₃ = 35

Then, Probability = 1 – 35/220 = 185/220 = 37/44

5. c

If 3 marbles are picked, then total Probability = ¹²C₃ = 220

Favorable no of cases = ⁵C₂ * ³C₁ = 30

Then, Probability = 30/220 = 3/22

6. a

If 4 marbles are picked, then total Probability = ¹²C₄ =495

Favorable no of cases = ⁴C₂ * ³C₂ = 18

Then, Probability = 18/495 = 2/55

7. b

If 4 marbles are picked, then total Probability = ¹²C₄ =495

Favorable no of cases = ³C₁ * ⁵C₂ * ⁴C₁ = 120

Then, Probability = 120/495 = 8/33

Thanks!!