# Quants Questions: Probability Set 5

Hello Aspirants. Welcome to Online Maths in AffairsCloud.com. Here we are creating question sample in Probability, which is common for all the competitive exams. We have included Some questions that are repeatedly asked in exams !!

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 ?
a) 7/15
b) 8/15
c) 11/15
d) 13/15
Solution :
PF + FP (P = pass, F = fail)
1/3*2/5 + 2/3*3/5 = 8/15

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 ?
a) 17/22
b) 19/22
c) 21/22
d) 15/22
Solution :
sol = 1 – no boy is selected
1 – 6c4/11c4 = 21/22

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 ?
a) 11/18
b) 13/18
c) 15/18
d) 17/18
Solution :
1 – 1/2*2/3*5/6 = 13/18

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 ?
a) 1/3
b) 1/4
c) 1/5
d) 2/3
Solution :
5c1/15c1 = 1/3

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 ?
a) 110/343
b) 120/343
c) 18/49
d) 139/343
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

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 ?
a) 1/4
b) 1/5
c) 1/6
d) 1/7
Solution :
Total number of outcome = 6*5*4*3*2
Favourable outcome = 5*4*3*2. So, P = 1/6

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 ?
a) 4/52*3/51
b) 4/51*3/52
c) 4/52*4/51
d) 3/52*3/51
Solution :4/52*4/51

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 ?
a) 7/20
b) 9/20
c) 11/20
d) 13/20
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

9. (Q 9 -10) Three coins are tossed simultaneously.
Find out the probability that there is at least 2 heads ?
a) 1/2
b) 1/4
c) 1/6
d) 1/8
Solution :
Sol = Total outcomes = {HHH,HTH,HHT,THH,TTT,TTH,THT,HTT}
Favourable outcome = HHH, HTH, HHT,THH
Prob = 4/8 = 1/2

10. Find the probability that there is exactly two tails ?
a) 3/8
b) 5/8
c)7/8
d) 1/8