UPSC ONLINE ACADEMY

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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?

### 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?

### 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?

### 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?

### 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?

### 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