IMPORTANT PROBABILITY QUESTIONS
CBSE CLASS 12
Chapter 13.3 – Multiplication Theorem
1. A box contains 4 green, 8 blue and 3 red pens. A pen is drawn at random, its colour noted and
replaced. This is done three times. Find the probability that at least one pen drawn is red.
2. The probability of finding a green signal on a busy crossing on a given day is 0.3. Find the
probability of finding a green signal on two consecutive days out of three days.
3. Given two independent events A and B such that P(A)=0.3 and P(B)=0.6, find P(A' ∩ B').
4. The probability of students A and B coming to school on time are 2/7 and 4/7 respectively.
Assuming independence, find the probability that only one of them comes to school on time.
Chapter 13.4 – Independent Events
5. The chances that three persons A, B and C go to market are 30%, 60% and 50% respectively.
Find the probability that at least one of them will go to the market.
6. If A and B are two independent events with P(A)=1/3 and P(B)=1/4, find P(B'|A).
7. A problem is given to three students whose probabilities of solving it are 1/3, 1/4 and 1/6
respectively. If the events of solving the problem are independent, find the probability that at least
one of them solves it.
8. The probability that A hits a target is 1/3 and the probability that B hits it is 2/5. If both try
independently, find the probability that the target is hit.
9. A die has faces 1,2,3 marked in red and 4,5,6 in green. Let A be the event “number obtained is
even” and B be the event “number obtained is red”. Check whether A and B are independent.
Chapter 13.5 – Bayes’ Theorem (Very Important)
10. There are two bags. Bag I contains 1 red and 3 white balls and Bag II contains 3 red and 5
white balls. A bag is selected at random and a ball is drawn. Find the probability that the ball drawn
is red.
11. A purse contains 3 silver and 6 copper coins and another purse contains 4 silver and 3 copper
coins. A coin is drawn at random from one of the purses. Find the probability that it is a silver coin.
12. For a vacancy, 3000 candidates applied. Two-third were females. The probability of a male
getting distinction is 0.4 and that of a female is 0.35. Find the probability that a randomly chosen
candidate gets distinction.
13. It is known that 20% of students in a school have above 90% attendance and 80% are irregular.
Past records show that 80% of students with above 90% attendance and 20% of irregular students
get A grade. A student is chosen at random and is found to have A grade. Find the probability that
the student is irregular.
14. A card is lost from a well-shuffled deck of 52 cards. From the remaining cards, a card is drawn
and found to be a king. Find the probability that the lost card was a king.
15. Out of two bags, bag A contains 2 white and 3 red balls and bag B contains 4 white and 5 red
balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability
that it was drawn from bag B.
CBSE CLASS 12
Chapter 13.3 – Multiplication Theorem
1. A box contains 4 green, 8 blue and 3 red pens. A pen is drawn at random, its colour noted and
replaced. This is done three times. Find the probability that at least one pen drawn is red.
2. The probability of finding a green signal on a busy crossing on a given day is 0.3. Find the
probability of finding a green signal on two consecutive days out of three days.
3. Given two independent events A and B such that P(A)=0.3 and P(B)=0.6, find P(A' ∩ B').
4. The probability of students A and B coming to school on time are 2/7 and 4/7 respectively.
Assuming independence, find the probability that only one of them comes to school on time.
Chapter 13.4 – Independent Events
5. The chances that three persons A, B and C go to market are 30%, 60% and 50% respectively.
Find the probability that at least one of them will go to the market.
6. If A and B are two independent events with P(A)=1/3 and P(B)=1/4, find P(B'|A).
7. A problem is given to three students whose probabilities of solving it are 1/3, 1/4 and 1/6
respectively. If the events of solving the problem are independent, find the probability that at least
one of them solves it.
8. The probability that A hits a target is 1/3 and the probability that B hits it is 2/5. If both try
independently, find the probability that the target is hit.
9. A die has faces 1,2,3 marked in red and 4,5,6 in green. Let A be the event “number obtained is
even” and B be the event “number obtained is red”. Check whether A and B are independent.
Chapter 13.5 – Bayes’ Theorem (Very Important)
10. There are two bags. Bag I contains 1 red and 3 white balls and Bag II contains 3 red and 5
white balls. A bag is selected at random and a ball is drawn. Find the probability that the ball drawn
is red.
11. A purse contains 3 silver and 6 copper coins and another purse contains 4 silver and 3 copper
coins. A coin is drawn at random from one of the purses. Find the probability that it is a silver coin.
12. For a vacancy, 3000 candidates applied. Two-third were females. The probability of a male
getting distinction is 0.4 and that of a female is 0.35. Find the probability that a randomly chosen
candidate gets distinction.
13. It is known that 20% of students in a school have above 90% attendance and 80% are irregular.
Past records show that 80% of students with above 90% attendance and 20% of irregular students
get A grade. A student is chosen at random and is found to have A grade. Find the probability that
the student is irregular.
14. A card is lost from a well-shuffled deck of 52 cards. From the remaining cards, a card is drawn
and found to be a king. Find the probability that the lost card was a king.
15. Out of two bags, bag A contains 2 white and 3 red balls and bag B contains 4 white and 5 red
balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability
that it was drawn from bag B.
