**Probability Questions for RRB Group-D PDF**

Download Top-10 RRB Group-D Probability Questions PDF. RRB GROUP-D Maths questions based on asked questions in previous exam papers very important for the Railway Group-D exam.

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**Question 1: **An unbiased coin is tossed 4 times. What is the probability that there are at least 3 heads?

a) 5/32

b) 1/4

c) 5/16

d) 1/2

**Question 2: **Find the probability of getting a prime number on throwing an unbiased die.

a) 2/3

b) 1/2

c) 5/6

d) 3/4

**Question 3: **A bag contains 5 red balls, 2 blue balls and 3 black balls. Two balls are selected from the bag. Find the probability that both the balls are red?

a) 2/9

b) 4/9

c) 5/9

d) 1/9

**Question 4: **Find the probability of forming a 4 letter words out of the letter A, C, E, I, G, H, Z, W such that the first letter is W.

a) 3/8

b) 1/8

c) 3/4

d) 4/5

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**Question 5: **Find the probability of obtaining 3 heads if 4 coins are tossed together?

a) 1/4

b) 3/8

c) 2/5

d) 1/2

**Question 6: **Find the probability of obtaining a green ball and a yellow ball from the bag containg 5 green balls, 3 yellow balls and 2 red balls if two balls are picked up from the bag?

a) 2/5

b) 3/5

c) 2/3

d) 1/3

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**Question 7: **Find the probability of forming a 7 letter words with letters E,R,Q,G,R,R,Q with each letter used exactky once and all the R’s come together?

a) 1/14

b) 2/7

c) 1/7

d) 3/14

**Question 8: **Find the probability of forming a 8 letter word with letters A,C,G,E,I,F,D,K such that each letter is used exactly once and all the vowels come together?

a) 1/7

b) 5/56

c) 1/14

d) 3/28

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**Question 9: **There are flags of three different colours namely Red, Yellow and Green. A code is to be made consisting of these three different flags in any order. Find the probability of forming a code having flag of yellow colour at the first place?

a) 1/3

b) 2/3

c) 4/5

d) 5/6

**Question 10: **A bag contains 5 black balls, 3 yellow balls, 5 blue balls and 2 red balls. A ball is drawn out from the bag and it is found to be red. Now another ball is drawn out from the bag. Find the probability of the ball being red?

a) 1/7

b) 1/14

c) 3/14

d) 2/7

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**Answers & Solutions:**

**1) Answer (C)**

For each toss of the coin, there are 2 possibilities. So, the total number of possibilities for 4 tosses of the coin is $2^4$ = 16

Number of ways of arranging 3 heads and 1 tail = 4

Number of ways of arranging 4 heads = 1

So, the required probability is 5/16

**2) Answer (B)**

From 1-6, only 2,3,5 are prime numbers.

Probability = 3/6 = 1/2

**3) Answer (A)**

Total number of balls = 5+2+3 = 10

When 2 balls are selected from a bag, number of ways of doing it =$^{10}C_2$

Number of ways of selecting red balls =$^{5}C_2$

Probability =$\frac{^{5}C_2}{^{10}C_2}$ = 2/9

**4) Answer (B)**

Number of ways of choosing 4 letters out of 8 letters and forming words with those 4 letters =$^8C_4*4!$

Now the first letter is W, we have to choose 3 letters out of 7 letters

Number of ways of choosing 3 letters out of 7 letters =$^7C_3*3!$

Probability =$\frac{^7C_3*3!}{^8C_4*4!}$ = 1/8

**5) Answer (A)**

Let H be the heads and T be the tails

P(H) = 1/2

P(T) = 1/2

There are 4 possibilites of obtaining 3 heads:HHHT,HHTH,HTHH,THHH,HHHT

Now the event of tossing 4 coins are independent,

P(3 heads occur) =$4*(1/2)^3(1/2)$ = 1/4

**6) Answer (D)**

Total number of balls in the bag = 5+3+2 = 10

Number of ways of picking 2 balls from the bag =$^{10}C_2$

Number of ways of picking up 2 balls such that one is green and other is yellow =$^{5}C_1*^{3}C_1 = 15$

Probability = 15/$^{10}C_2$ = 1/3

**7) Answer (C)**

Probability of forming a 7 letter word from the given words =$\frac{7!}{3!*2!}$

Now we have to calculate the number of ways of forming a 7 letter words in which all R occur together.

Consider all 3 R’s as one group.

Number of ways of forming all the words with one group of R’s and 4 other words =$\frac{5!}{2!}*\frac{3!}{3!}$

5!/2! refers to the number of ways of arranging 5 letters with 2 Q’s. 3!/3! refers to the number of ways of arranging R’s.

Probability =$\frac{\frac{5!}{2!}*\frac{3!}{3!}}{\frac{7!}{3!*2!}}$ = 1/7

**8) Answer (D)**

In these letters, no letter is used more than once. So the total no. of words formed with the letters A,C,G,E,I,F,D,K is 8! Ways.

A,C,G,E,I,F,D,K

In this group A, E, I are vowels. Let us consider them as one group. This group along with the other 5 letters can be arranged in (5+1)! = 6! Ways.

Now this group contains 3 letters which can be arranged in 3! Ways

Total number of ways of arranging all the letter such that vowels come together = 3!*6!

Probability = 3!*6!/8! = 6/56 = 3/28

**9) Answer (A)**

The flags are of three different colors namely Red, Yellow and Green. These 3 flags can be arranged in 3! Ways = 6 ways

When the yellow colored flag is at the first position, number of ways of forming a flag = 2! = 2

Probability = 2/6 = 1/3

**10) Answer (B)**

Let B be the event of drawing out the first ball which was red and A be the event of drawing out the second ball which is red.

There are two red balls in the bag initially out of the total of 15 balls.

One red ball is taken out in the first instance. Now only one red ball remains out of 14 remaining balls.

P(A/B) = 1/14

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