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# PROBABILITY, PERMUTATION & COMBINATION SET 1

Q.1 A bag contains four black and five red balls, if three balls are picked at random one after another WITH replacement, what is the chance that they’re all black?

A) 64/729

B) 64/730

C) 63/729

D) 63/730

Ans. A

With replacement means you pick up a ball note down its color and then put it back in the bag again. So Total Number of balls remain same for each event. And Hence probability of picking a black ball (4/9) remains the same in every case.
1st Pick up:4/9;
2nd Pick up: 4/9 ;because we put the ball back in the bag, So probability is same as “1st Pick”.
3rd Pick up: 4/9 ;because we put the ball back in the bag.
So final probability
=1st x 2nd x 3rd
=4/9 x 4/9 x 4/9
=Cube of 4/9
=64/729

Q.2 If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non blue sector?

A) Green = 3/5 ; Non-blue = 4/5

B) Green = 2/5 ; Non-blue = 3/5

C) Green = 4/5 ; Non-blue = 3/5

D) Green = 3/5 ; Non-blue = 2/5

Ans. A

Total number of events = 5

Q.3 A bag has 4 red balls and 2 yellow balls. (The balls are identical in all
respects other than colour). A ball is drawn from the bag without looking into the bag. What is probability of getting a red ball?

A) 2/3

B) 2/4

C) 2/5

D) 2/6

Ans. A

There are in all (4 + 2 =) 6 outcomes of the event. Getting a red ball
consists of 4 outcomes.

Therefore, the probability of getting a red ball is
4/6 = 2/3

Q.4 There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% students play both the games. What is the number of students who play neither cricket nor football?

A) 25

B) 20

C) 18

D) 15

Ans. B

100- (50+20+10)
= 100-80 = 20

Q.5 In a group of persons, 70% of the persons are male and 30% of the persons are
married. If two-sevenths of the males are married, what fraction of the females is
single?

A) 2/7

B) 1/3

C) 3/7

D) 2/3
Ans. D
Let total no. of persons =100
Therefore total no. of males= 70
Total no. of females= 30
Given that, no. of unmarried persons =30
So, Number of married males=
2/7 * 70=20
Therefore, No. of married females
=30-20 =10
Therefore, No. of unmarried females
=30-10 = 20
Therefore, Required fraction of single females=
20/30 = 2/3