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Download Probability Questions for XAT PDF – XAT Probability questions PDF by Cracku. Practice XAT solved Probability Questions paper tests, and these are the practice question to have a firm grasp on the Probability topic in the XAT exam. Top 20 very Important Probability Questions for XAT based on asked questions in previous exam papers.  The XAT question papers contain actual questions asked with answers and solutions.

Question 1: The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

a) 2222

b) 2442

c) 2592

d) 3333

Solution:

The number of 4-digit numbers possible using 1,1,2, and 4 is $\frac{4!}{2!}=12$

Number of 1’s, 2’s and 4’s in units digits will be in the ratio 2:1:1, i.e. 6 1’s, 3 2’s and 3 4’s.

Sum = 6(1) + 3(2) + 3(4) = 24

Similarly, in tens digit, hundreds digit and thousands digit as well.

Therefore, sum = 24 + 24(10) + 24(100) + 24(1000) = 24(1111)

Mean = $\frac{24\left(1111\right)}{12}=2222$

Question 2: The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit at most once, is

a) 1440

b) 1200

c) 1480

d) 1420

Solution:

Case 1: 4-digit numbers

Given digits – 0, 1, 2, 3, 4, 5

_, _, _, _

As the numbers should be greater than 2000, first digit can be 2, 3, 4 and 5.

For remaining digits, we need to arrange 3 digits from the remaining 5 digits, i.e. 5*4*3 = 60 ways

Total number of possible 4-digit numbers = 4*60 = 240

Case 2: 5-digit numbers

_, _, _, _, _

First digit cannot be zero.

Therefore, total number of cases = 5*5*4*3*2 = 600

Case 3: 6-digit numbers

_, _, _, _, _, _

First digit cannot be zero.

Therefore, total number of cases = 5*5*4*3*2*1 = 600

Total number of integers possible = 600 + 600 + 240 = 1440

Question 3: The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is

Solution:

Let the number of balloons each child received be 2a, 2b, 2c and 2d

2a + 2b + 2c + 2d = 20

a + b + c + d = 10

Each of them should get more than zero balloons.

Therefore, total number of ways = $(n-1)_{C_{r-1}}=(10-1)_{C_{4-1}}=9_{C_3}=84$

Question 4: A bag contains 6 red balls, 11 yellow balls and 5 pink balls. If two balls are drawn at a random from the bag, one after another. What is the probability that the first ball drawn was red and the second ball drawn was yellow in colour?

a) $\frac{3}{14}$

b) $\frac{5}{7}$

c) $\frac{1}{7}$

d) $\frac{1}{14}$

Solution:

There are 6 red balls, 11 yellow balls and 5 pink balls

Total number of balls = 6 + 11 + 5 = 22

Probability of selecting red ball = $\frac{6}{22}$

After selecting one ball, there are 21 balls left

Probability of selecting yellow ball = $\frac{11}{21}$

Therefore, probability = $\frac{6}{22}\times\ \frac{11}{21}$ = $\frac{1}{7}$

Question 5: In a bag there are 15 red balls and 10 green balls. Three balls are selected at random. The probability of selecting 2 red balls and 1 green ball is :

a) $\frac{21}{46}$

b) $\frac{25}{117}$

c) $\frac{3}{25}$

d) $\frac{1}{50}$

Solution:

Number of ways of selecting 2 red balls and 1 green ball = $15_{C_2}.\ 10_{C_1}$

Number of ways of selecting 3 balls = $25_{C_3}$

Probability of selecting 2 red balls and 1 green ball = $\ \frac{15_{C_2}.10_{C_1}}{25_{C_3}}$ = $\frac{21}{46}$

Question 6: The following five candidates have applied for a position in an organisation: Male 30 years, Male 32 years, Female 45 years, Female 20 years, and Male 40 years. What is the probability that the candidate selected for the position will be either female or over 35 years?

a) 4/5

b) 2/5

c) 1/5

d) 3/5

Solution:

Female – A
above 35 years – B
n(A $\cup$ B ) = n(A)+n(B) – n (A $\cap$ B) = 2 + 2 – 1 = 3
Probability = $\frac{3}{5}$

Question 7: In a class of 45 students, 25 are girls. In a test, 30 students scored above 90% marks and 18 of them are girl students. A student is selected at random. The probability of selecting a girl scoring above 90% marks is___________

a) 18/45

b) 12/45

c) 18/30

d) 30/45

Solution:

It is given,
Total number of students = 45
Number of girls who scored above 90% marks = 18
Therefore, probability = $\frac{18}{45}\$

Question 8: In a charity show, tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected randomly will have a number with a hundredth digit as two?

a) 100/250

b) 99/249

c) 100/249

d) 99/250

Solution:

350 = 101 + (n-1)1
n = 250
Total number of tickets = 250
There are 100 tickets(200 to 299) between the tickets 101 and 350 whose hundredth digit is 2.
Probability = $\ \frac{100}{250}$

Question 9: What is the probability that a leap year has 53 Sundays and 53 Mondays?

a) 2/7

b) 1

c) 0

d) 1/7

Solution:

Number of days in leap year = 366
There are 2 odd days in a leap year. For a year to have 53 sundays and 53 mondays, 2 odd days should be sunday and monday.
This is only possible when the first day of the year is sunday.
Therefore, the probability of the first day is sunday = $\frac{1}{7}$

Question 10: There is a shooting event organised by the SBT youth Club to select the best candidate who will qualify to participate in Eklavya championship. The shooting board is designed by using 4 concentric circles of radii 2 inch, 3 inch, 5 inch and 9 inch. What is the probability that the participant will shoot only in the second ring [from the outside] to qualify for Eklavya championship.

a) $\frac{16}{25}$

b) $\frac{20}{81}$

c) $\frac{20}{56}$

d) $\frac{16}{81}$

The required probability = $\frac{\pi\left(5\right)^2-\pi\left(3\right)^2}{\pi\left(9\right)^2}=\frac{25-9}{81}=\frac{16}{81}$