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 =

^{12}C_{3 }= 220Favorable no of cases =

^{4}C_{3}+^{3}C_{3 }= 4 + 1 = 5Then, Probability = 5/220 = 1/44

**2. d**

If 2 marbles are picked, then total Probability =

^{12}C_{2 }= 66Favorable no of cases =

^{4}C_{2}= 6Then, Probability = 6/66 = 1/11

**3. a**

If 2 marbles are picked, then total Probability =

^{12}C_{2 }= 66Favorable no of cases without blue (4+3 = 7) =

^{7}C_{2 }= 21Then, Probability = 21/66 = 7/22

**4. c**

If 3 marbles are picked, then total Probability =

^{12}C_{3 }= 220Favorable no of cases without blue (4+3 = 7) =

^{7}C_{3 }= 35Then, Probability = 1 – 35/220 = 185/220 = 37/44

**5. c**

If 3 marbles are picked, then total Probability =

^{12}C_{3 }= 220Favorable no of cases =

^{5}C_{2 }*^{3}C_{1 }= 30Then, Probability = 30/220 = 3/22

**6. a**

If 4 marbles are picked, then total Probability =

^{12}C_{4 }=495Favorable no of cases =

^{4}C_{2 }*^{3}C_{2 }= 18Then, Probability = 18/495 = 2/55

**7. b**

If 4 marbles are picked, then total Probability =

^{12}C_{4 }=495Favorable no of cases =

^{3}C_{1 }*^{5}C_{2 }*^{4}C_{1 }= 120Then, Probability = 120/495 = 8/33

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