## Probability Questions for IBPS PO

### Probability Questions for IBPS PO 2016 Exam

**1.** A five digit number is formed with the digits 0,1,2,3 and 4 without repetition. Find the chance that the number is divisible by 5. **(IBPS PO Mains 2016)**

(a) 3/5

(b) 1/5

(b) 2/5

(d) 4/5

(e) None of these

**2.** A box contains 5 green, 4 yellow and 3 white marbles. Three marbles are drawn at random. What is the probability that they are not of the same colour ? **(IBPS PO Mains 2016)**

(a) 40/44

(b) 44/41

(c) 41/44

(d) 40/39

(e) 44/39

**3.** From a pack of 52 cards, 3 cards are drawn together at random, What is the probability of both the cards are king ? **(IBPS PO Mains 2016)**

(c) 5225

(e) None of these

**Probability Questions for IBPS PO 2016 Answers**

**1.** (b)

5 digit number = 5! = 120

Divisible by 5 then the last digit should be 0

Then the remaining position have the possibility = 4! = 24

P = (4!/5!) = 24/120 = 1/5

**2.** (c)

n(E) = ^{5}C_{3} + ^{4}C_{3} + ^{3}C_{3} =10 + 4 +1 = 15

n(S) = ^{12}C_{3}= 220

Required probability

**3.** (b)

### Probability Questions for IBPS PO 2015 Exam

**Study the following information carefully to answer the questions that follow-**

A committee of five members is to be formed out of 5 Males, 6 Females and 3 Children. In how many different ways can it be 58. done if-? **(IBPS PO Prelim 2015)**

**1.** The committee should consist of 2 Males, 2 Females and 1 Child?

(a) 450

(b) 225

(c) 55

(d) 90

(e) None of these

**2.** The committee should include all the 3 Childs?

(a) 90

(b) 180

(c) 21

(d) 55

(e) None of these

**3.** In how many different ways can 4 boys and 3 girls be arranged in a row such that all the boys stand together and all the girls stand together ?** (IBPS PO Prelim 2015)**

(a) 75

(b) 576

(c) 288

(d) 24

(e) None of these

**4.** In how many different ways can the letters of the word ‘PRIDE’ be arranged ? **(IBPS PO Main 2015)**

(a) 60

(b) 120

(c) 15

(d) 360

(e) None of these

**5.** There are 8 brown balls, 4 orange balls and 5 black balls in a bag. Five balls are chosen at random. What is the probability of their being 2 brown balls, 1 orange ball and 2 black balls?**(IBPS PO Main 2015)**

**Probability Questions for IBPS PO 2015 Answers**

**1.** (a)

Number of ways = ^{5}C_{2} × ^{6}C_{2} × ^{3}C_{1}= 450

**2.** (d)

Number ofways = ^{11}C_{2} × ^{5}C_{2} = 55.

**3.** (c)

Required number of ways = 4! × 31 × 2! = 288.

**4.** (b)

‘PRIDE’ has five different letters.

So, it can be arranged in 5 ! = 120 ways

**5.** (c)

Total possible outcomes = ^{17}C_{5}

Total favourable outcomes = ^{8}C_{2} × ^{4}C_{1} × ^{5}C_{2}

Required probability

### Probability Questions for IBPS PO 2014 Exam

**1.** In how many different ways can the letters of the word ‘LEADING’ be arranged in such a way that the vowels always come together? **(IBPS PO/MT 2014)**

(a) 360

(b) 480

(c) 720

(d) 5040

(e) None of these

**2.** In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is: **(IBPS PO/MT 2014)**

(e) None of these

**3.** Gauri went to the stationery and bought things worth ’25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?** (IBPS PO/MT 2014)**

(a) ₹ 15

(b) ₹ 15.70

(c) ₹ 19.70

(d) ₹ 20

(e) None of these

**Probability Questions for IBPS PO 2014 Answers**

**1.** (c)

The word ‘LEADING’ has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

∴ Required number of ways = (120 × 6) = 720.

**2.** (a)

Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

Then, n(S) = Number ways of selecting 3 students out of 25

= ^{25}C_{3}

n(E) = (^{10}C_{1} × ^{15}C_{2})

= 1050

**3.** (c)

Let the amount taxable purchases be Rs. x.

Then, 6 % of

∴ Cost of tax free items = Rs.[25 – (5 + 0.30)] = ₹ 19.70

### Probability Questions for IBPS PO 2012 Exam

**1.** In how many different ways can the letters of the word ‘THERAPY’ be arranged so that the vowels never come together ?** (IBPS PO/MT 2012)**

(a) 720

(b) 1440

(c) 5040

(d) 3600

(e) 4800

**2.** A bag contains 13 white and 7 black balls. Two balls are drawn at random. What is the probability that they are of the same colour ?** (IBPS PO/MT 2012)**

**Probability Questions for IBPS PO 2012 Answers**

**1.** (d)

No. of vowels in the word THERAPY

= 2 i.e. E and A

In such cases we treat the group of two vowels as one entity or one letter because they are supposed to always come together. Thus, the problem reduces to arranging 6 letters i.e. T, H, R, P, Y and in 6 vacant places.

No. of ways 6 letters can be arranged in 6 places = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

But the vowels can be arranged themselves in 2 different ways by interchanging their position. Hence, each of the above 720 arrangements can be written in 2 ways.

∴ Required no. of total arrangements when two vowels are together = 720 × 2 = 1440

Total no. of arrangements of THERAPY = 7!

= 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

No. of arrangement when vowels do not come together

= 5040 – 1440 = 3600

**2.** (d)

No. of ways of getting 2 white balls = ^{13}C_{2}

No. of ways of getting 2 black balls = ^{7}C_{2}

Probability of getting 2 same colour ball

### Probability Questions for IBPS PO 2011 Exam

**Study the given information carefully to answer the questions that follow.**

An urn contains 4 green, 5 blue, 2 red and 3 yellow marbles.

**1.** If four marbles are drawn at random, what is the probability that two are blue and two are red?

(e) None of these

**2.** If eight marbles are drawn at random, what is the probability that there are equal number of marbles of each colour ?

(e) None of these

**3.** If two marbles are drawn at random, what is the probability that both are red or at least one is red ?

(e) None of these

**4.** If three marbles are drawn at random, what is the probability that at least one is yellow ?

(e) None of these

**5.** If three marbles are drawn at random, what is the probability that none is green ? (IBPS PO 2011)

(e) None of these

**Probability Questions for IBPS PO 2011 Answers**

**1.** (a)

According to question.

and

∴ Required probability

**2.** (c)

According to the question

and n(E) = ^{4}C_{2} × ^{5}C_{2} × ^{2}C_{2} × ^{3}C_{2}

∴ Required probability

**3.** (e)

According to the question

∴ Probability of at least one red ball

**4.** (b)

According to the question

∴ Required probability

**5.** (e)

According to the question

and

∴ Required probability

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