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This mock test of Probability - MCQ 5 for Quant helps you for every Quant entrance exam.
This contains 20 Multiple Choice Questions for Quant Probability - MCQ 5 (mcq) to study with solutions a complete question bank.
The solved questions answers in this Probability - MCQ 5 quiz give you a good mix of easy questions and tough questions. Quant
students definitely take this Probability - MCQ 5 exercise for a better result in the exam. You can find other Probability - MCQ 5 extra questions,
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QUESTION: 1

The probability of two persons of passing the interview are 1/3 and 3/5. Then calculate the probability that only one of them pass the interview ?

Solution:

PF + FP (P = pass, F = fail)

1/3*2/5 + 2/3*3/5 = 8/15

QUESTION: 2

Among a group of 5 boys and 6 girls, 4 members is to be selected for an event. Find the probability that at least one boy is selected ?

Solution:

sol = 1 – no boy is selected

1 – 6c4/11c4 = 21/22

QUESTION: 3

The probability that the problem will be solved by three persons are 1/2, 1/3 and 1/6. Find the probability that the problem is solved ?

Solution:

1 – 1/2*2/3*5/6 = 13/18

QUESTION: 4

A urn contains 4 red balls, 5 green balls and 6 white balls, If one ball is drawn at random, find the probability that it is neither red nor white ?

Solution:

5c1/15c1 = 1/3

QUESTION: 5

An elevator starts with 4 passenger and stops at 7 floors of an apartment. Find the probability that all 4 passengers travel to different floor ?

Solution:

Total number of outcomes = 7*7*7*7

Favourable outcome = 7*6*5*4

P = (7*6*5*4)/7*7*7*7 = 120/343

QUESTION: 6

A five digit number is formed from the numbers 1,3,5,7,8 and 9 without repeating the numbers. Find the probability that the number is divisible by 5 ?

Solution:

Total number of outcome = 6*5*4*3*2

Favourable outcome = 5*4*3*2. So, P = 1/6

QUESTION: 7

From a deck of 52 cards, a card is selected and without replacing the card a new card is selected. Find out the probability that the first card is an ace and second card is a king ?

Solution:

4/52*4/51

QUESTION: 8

The probability that a person will be alive after 20 years is 1/4 and that of his wife is 2/5. Find out the probability that both are not alive after 20 years ?

Solution:

prob. That man is not alive = 3/4 and that of his wife = 3/5

Prob. That both will be dead = 3/4*3/5 = 9/20

QUESTION: 9

Three coins are tossed simultaneously.

**Q. **

**Find out the probability that there is at least 2 heads ?**

Solution:

= Total outcomes = {HHH,HTH,HHT,THH,TTT,TTH,THT,HTT}

Favourable outcome = HHH, HTH, HHT,THH

Prob = 4/8 = 1/2

QUESTION: 10

Three coins are tossed simultaneously.

**Q. **

**Find the probability that there is exactly two tails ?**

Solution:

Favourable outcome = TTH, THT, HTT

So, prob. = 3/8

QUESTION: 11

An urn contain 6 orange, 4 green,3 pink and 4 black balls

**Q. **

**If 3 balls are picked at random, what is the probability that all are pink ?**

Solution:

17C3 = 17*16*15/3*2*1 = 4080/6 = 680

3C3 = 1

P = 1/680

QUESTION: 12

An urn contain 6 orange, 4 green,3 pink and 4 black balls

**Q. **

**If 5 balls are picked at random, what is the probability that none are orange ?**

Solution:

17C5 = 17*16*15*14*13/5*4*3*2*1 = 742560/120 = 6188

11C5 = 11*10*9*8*7/5*4*3*2*1 = 55440/120 = 462

P = 462/6188 = 33/442

QUESTION: 13

An urn contain 6 orange, 4 green,3 pink and 4 black balls.

**Q. **

**If 3 balls are drawn at random, what is the probability that 1 is green and the other 2 are black ?**

Solution:

17C3 = 17*16*15/3*2*1 = 4080/6 = 680

4C1 × 4C2 = 4*4*3/2*1 = 24

P = 24/680 = 3/85

QUESTION: 14

There are 8 positive numbers and 6 negative numbers. 4 numbers are chosen at random and multiplied. Find the probability that the product is a positive number ?

Solution:

14C4 = 14*13*12*11/4*3*2*1 = 1001

4 No positive+4 no negative + (2 no positive * 2 no negative)

= 6C4 + 8C4 +(6C2 ×8C2) = 15+70+15*28 = 505

P = 505/1001

QUESTION: 15

A five digit number is formed with the digit 1,2,3,4 and 5 without repetition. Find the chance that the number is divisible by 5 ?

Solution:

5! = 5*4*3*2*1 = 120

4! = 4*3*2*1 = 24

P = 24/120 = 1/5

QUESTION: 16

A bag contains 6 red, 5 blue and 2 green balls. If 2 balls are picked at random, what is the probability that both are green?

Solution:

13C2 = 13*12/2 =78

2C2 = 1

P = 1/78

QUESTION: 17

If You toss a coin and roll a die. What is the probability of getting a head and a 3 on the die?

Solution:

1/2 * 1/6 = 1/12

QUESTION: 18

From a pack of 52 cards, 3 cards are drawn. What is the probability that one is ace, one is queen and one is jack?

Solution:

=4C1×4C1×4C1 / 52C3

=4×4×4 / 22100

=16/5525

QUESTION: 19

Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one dice and multiple of 3 on the other dice.

Solution:

n(S) = 36

n(E) = (2,3),(2,6),(4,3),(4,6),(6,3),(6,6),(3,2),(6,2),(3,4),(6,4),(3,6)

P = 11/36

QUESTION: 20

Two dice are tossed. The probability that the total score is a prime number is

Solution:

E = (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5)

n(E) = 15

n(S) = 6*6 = 36

P = 15/36 = 5/12

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