Class 12 Maths ISC Probability Board Questions
Here we provide Class 12 Maths important notes,board questions and predicted questions with Answers for chapter Probability. These important notes,board questions and predicted questions are based on ISC board curriculum and correspond to the most recent Class 12 Maths syllabus. By practising these Class 12 materials, students will be able to quickly review all of the ideas covered in the chapter and prepare for the Class 12 Board examinations.
2016
Q1
A pair of dice is thrown—What is the probability of getting an even number on the first die or a
total of 8?
solutions
solutions
Q2
(a) A committee of 4 persons has to be chosen from 8 boys and 6 girls, consisting of at least one
girl. Find the probability that the committee consists of more girls than
boys.
(b) An urn contains 10 white and 3 black balls while another urn contains 3 white and 5 black balls. Two balls are drawn from the first urn and put into the second urn and then a ball is drawn from the second um. Find the probability that the ball drawn from the second um is a white ball.
solutions
(b) An urn contains 10 white and 3 black balls while another urn contains 3 white and 5 black balls. Two balls are drawn from the first urn and put into the second urn and then a ball is drawn from the second um. Find the probability that the ball drawn from the second um is a white ball.
solutions
2017
Q1
A problem is given to three students whose chances of solving it are 1/4,1/5 and 1/3 respectively.
Find the probability that the problem is solved.
solutions
solutions
Q2
In a class of 60 students, 30 opted for Mathematics, 32 opted for Biology and 24
opted for both Mathematics and Biology. If one of these students is selected at
random, find the probability that:
(i) The student opted for Mathematics or Biology.
(ii) The student has opted neither Mathematics nor Biology.
(iii) The student has opted Mathematics but not Biology.
(b) Bag A contains 1 white, 2 blue and 3 red balls. Bag B contains 3 white, 3 blue and 2 red balls. Bag C contains 2 white, 3 blue and 4 red balls. One bag is selected at random and then two balls are drawn from the selected bag. Find the probability that the balls drawn are white and red.
solutions
(i) The student opted for Mathematics or Biology.
(ii) The student has opted neither Mathematics nor Biology.
(iii) The student has opted Mathematics but not Biology.
(b) Bag A contains 1 white, 2 blue and 3 red balls. Bag B contains 3 white, 3 blue and 2 red balls. Bag C contains 2 white, 3 blue and 4 red balls. One bag is selected at random and then two balls are drawn from the selected bag. Find the probability that the balls drawn are white and red.
solutions
Q3
(a) A fair die is rolled. If face I turns up, a ball is drawn from Bag A. If face 2 or 3
turns up, a ball is drawn from Bag B. If face 4 or 5 or 6 turns up, a ball is drawn
from Bag C. Bag A contains 3 red and 2 white balls, Bag B contains 3 red and 4
white balls and Bag C contains 4 red and 5 white balls. The die is rolled, a Bag is
picked up and a ball is drawn. If the drawn ball is red, what is the probability that
it is drawn from Bag B?
(b) An urn contains 25 balls of which 10 balls are red and the remaining green. A ball is drawn at random from the urn, the colour is noted and the ball is replaced. If 6 balls are drawn in this way, find the probability that:
(i) All the balls are red.
(ii) Not more than 2 balls are green.
(iii) Number of red balls and green balls are equal.
solutions
(b) An urn contains 25 balls of which 10 balls are red and the remaining green. A ball is drawn at random from the urn, the colour is noted and the ball is replaced. If 6 balls are drawn in this way, find the probability that:
(i) All the balls are red.
(ii) Not more than 2 balls are green.
(iii) Number of red balls and green balls are equal.
solutions
2018
Q1
If A and B are events such that P(A) =1/2, P(B)= 1/3 and P(AnB)=1/4, then find:
(a) P(A/B)
(b) P(B/A)
In a race, the probabilities of A and B winning the race are 1/3 and 1/6 respectively. Find the probability of neither of them winning the race.
solutions
(a) P(A/B)
(b) P(B/A)
In a race, the probabilities of A and B winning the race are 1/3 and 1/6 respectively. Find the probability of neither of them winning the race.
solutions
Q2
A speaks fruth in 60% of the cases, while B in 40% of the cases. In what percent of cases
are they likely to contradict each other in stating the same fact?
solutions
solutions
Q3
From a lot of 6 items containing 2 defective items, a sample of 4 items are drawn at
random. Let the random variable X denote the number of defective items in the sample.
If the sample is drawn without replacement, find:
(a) The probability distribution of X
(b) Mean of X
(c) Variance of X
solutions
(a) The probability distribution of X
(b) Mean of X
(c) Variance of X
solutions
2019
Q1
(ix) Two balls are drawn from an urn containing 3 white, 5 red and 2 black balls, one
by one without replacement. What is the probability that at least one ball is red?
(x) If events A and B are independent, such that P(A) = 3/5, P(B)=2/3 find P (A∪B).
solutions
(x) If events A and B are independent, such that P(A) = 3/5, P(B)=2/3 find P (A∪B).
solutions
Q2
Bag A contains 4 white balls and 3 black balls, while Bag B contains 3 white balls and 5
black balls. Two balls are drawn from Bag A and placed in Bag B. Then, what is the
probability of drawing a white ball from Bag B?
solutions
solutions
Q3
Given three identical Boxes A, B and C, Box A contains 2 gold and 1 silver coin,
Box B contains 1 gold and 2 silver coins and Box C contains 3 silver coins. A
person chooses a Box at random and takes out a coin. If the coin drawn is of
silver, find the probability that it has been drawn from the Box which has the
remaining two coins also of silver.
OR
Determine the binomial distribution where mean is 9 and standard deviation is 3/2. Also, find the probability ofobtaining at most one success.
solutions
OR
Determine the binomial distribution where mean is 9 and standard deviation is 3/2. Also, find the probability ofobtaining at most one success.
solutions
2020
Q1
(ix) A bag contains 5 white, 7 red and 4 black balls. If four balls are drawn one by one
with replacement, what is the probability that none is white?
(x) Let A and B be two events such that P(A)=1/2,P(B)=p and P(A⋃B)=3/5
find 'p' if A and B are independent events.
solutions
(x) Let A and B be two events such that P(A)=1/2,P(B)=p and P(A⋃B)=3/5
find 'p' if A and B are independent events.
solutions
Q2
Three persons A, B and C shoot to hit a target. Their probabilities of hitting the target 5/6,4/5
and 3/4 respectively. Find the probability that:
(i) Exactly two persons hit the target.
(ii) At least one person hits the target.
solutions
(i) Exactly two persons hit the target.
(ii) At least one person hits the target.
solutions
Q3
The probability that a bulb produced ina factory will fuse after 150 days of use is 0•05. Find
the probability that out of 5 such bulbs:
(i) None will fuse after 150 days of use.
(ii) Not more than one will fuse after 150 days of use.
(iii) More than one will fuse after 150 days of use.
(iv) At least one will fuse after 150 days of use.
solutions
(i) None will fuse after 150 days of use.
(ii) Not more than one will fuse after 150 days of use.
(iii) More than one will fuse after 150 days of use.
(iv) At least one will fuse after 150 days of use.
solutions
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