Hello friends, I hope your preparation for IBPS Clerical is going on at full speed. And extra push to those who have their exams this weekend!

Probability is a must have in your armour – it is easy and commonly asked.

So, there is no reason why we shouldn’t revise this topic before the exam – 10 questions coming up!

Solution: In this question – we need atleast one woman in the set of chosen two people – okay.

This is how we could do it – 1

1

1

So our possible events are these above three … and any of the three can happen.

All three possibilities of combination will not happen together – only one can happen and so … the

P(E) = (5/13 x 8/12) + (8/13 x 5/12) + (5/13 x 4/12) = 25/39

Our answer is 25/39.

Note: The denominator in the second fractions is always 12. Why? Simply because the first fractions [5/13, 8/13, 5/13] means choosing 1 out of them – and since one is being chosen – it’ll leave 12 [13-1]!

Okay, now you solve…

Ans.: 20/39

(a) the balls drawn are replaced before the next ball is picked

(b) the balls drawn are not replaced

Ans.: (a) 8/13 x 8/13 x 8/13

(b) 8/13 x 7/12 x 6/11

(i)there is at least one ‘6’;

(ii)the sum is 5.

(ii)1/9

Probability is a must have in your armour – it is easy and commonly asked.

So, there is no reason why we shouldn’t revise this topic before the exam – 10 questions coming up!

### Question 1

Out of 13 applicants for a job, there are 5 women and 8 men. Two persons are to be selected for the job. What is the probability that at least one of the selected persons will be a woman?Solution: In this question – we need atleast one woman in the set of chosen two people – okay.

This is how we could do it – 1

^{st}is a woman and 2^{nd}a man*OR*1

^{st}a man and 2^{nd}a woman*OR*1

^{st}is a woman and 2^{nd}is also a woman. (We need atleast one woman! No ceiling on the max!)So our possible events are these above three … and any of the three can happen.

All three possibilities of combination will not happen together – only one can happen and so … the

__becomes important to note!__*OR*P(E) = (5/13 x 8/12) + (8/13 x 5/12) + (5/13 x 4/12) = 25/39

Our answer is 25/39.

Note: The denominator in the second fractions is always 12. Why? Simply because the first fractions [5/13, 8/13, 5/13] means choosing 1 out of them – and since one is being chosen – it’ll leave 12 [13-1]!

Okay, now you solve…

### Question 2

There are two bags containing white and black balls. In the first bag, there are 8 white and 6 black balls and in the second bag, there are 4 white and 7 black balls. One ball is drawn at random from any of these two bags. Find the probability of this ball being black.**Ans**: 41/77

### Question 3

Out of 40 consecutive integers, two are chosen at random. Find the probability that their sum is odd.Ans.: 20/39

### Question 4

From a bag containing 8 green and 5 red balls, three are drawn one after the other. Find the probability of all three balls being green if(a) the balls drawn are replaced before the next ball is picked

(b) the balls drawn are not replaced

Ans.: (a) 8/13 x 8/13 x 8/13

(b) 8/13 x 7/12 x 6/11

### Question 5

In rolling two dices, find the probability that,(i)there is at least one ‘6’;

(ii)the sum is 5.

**Ans**: (i)11/36

(ii)1/9

### Question 6

In a horse race there were 18 horses numbered 1-18. The probability that horse 1 would win is 1/6, that 2 would win is 1/10 and that 3 would win is 1/8. Assuming that a tie is impossible, find the chance that one of the three will win. [This is a great question – I hope you can do it!]**Ans**: 47/120

### Question 7

If among the executives who have subscribed to the Time magazine, an executive is picked at random. What is the probability that he has also subscribed to the Economist?**Ans**: 3/8

### Question 8

From a pack of 52 playing cards, three cards are drawn at random. Find the probability of drawing a king, a queen and jack. {Card question are always a must!}

**Ans**: 6/5525### Question 9

A group of investigators took a fair sample of 1972 children from the general population and found that there are 1000 boys and 972 girls. If the investigators claim that their research is so accurate that the sex of a newborn child can be predicted based on the ratio of the sample of the population, then what is the expectation in terms of the probability that a newborn child will be a girl?

[Hint: How many complete weeks in a normal year? 52! That means we have accounted for 52 x 7 = 364 days. ANormal year has 365 days and Leap year has 366 days.

Since, 52 weeks are a certainty – we know 52 Sundays will 100% occur! So we need to find the probability of either the 365

That is all for today guys. Hope you had those juices in your brain given a little extra something with today’s exercise.

**Ans**: 243/493### Question 10

Find a probability that a leap year chosen at random will have 53 Sundays.[Hint: How many complete weeks in a normal year? 52! That means we have accounted for 52 x 7 = 364 days. A

Since, 52 weeks are a certainty – we know 52 Sundays will 100% occur! So we need to find the probability of either the 365

^{th}and 366^{th}days being a Sunday!]**Ans**: 2/7That is all for today guys. Hope you had those juices in your brain given a little extra something with today’s exercise.

Have a good one!