Happy Teej - TEEJ2024

# Quant Mania: Probability (with Solution Key)

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!!