KC+CET PYQs for Conditional Probability with Solutions: Practice KCET Previous Year Questions

Updated on - Feb 16, 2026

Conditional Probability is an important topic in the Mathematics section in KCET exam. Practising this topic will increase your score overall and make your conceptual grip on KCET exam stronger.

This article gives you a full set of KCET PYQs for Conditional Probability with explanations for effective preparation. Practice of KCET Mathematics PYQs including Conditional Probability questions regularly will improve accuracy, speed, and confidence in the KCET 2026 exam.

KCET PYQs for Conditional Probability with Solutions

1.
A car manufacturing factory has two plants X and Y. Plant X manufactures 70% of cars and plant Y manufactures 30% of cars. 80% of cars at plant X and 90% of cars at plant Y are rated as standard quality. A car is chosen at random and is found to be standard quality. The probability that it has come from plant X is
- $\frac{56}{73}$
- $\frac{56}{84}$
- $\frac{56}{83}$
- $\frac{56}{79}$
View Solution
2.
If A and B are the two events such that $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$ and $P(A|B) = \frac{1}{4}$, then $P(A' \cap B')$ is
- $\frac{1}{4}$
- $\frac{1}{12}$
- $\frac{3}{16}$
- $\frac{3}{4}$
View Solution
3.
Given that A and B are two events such that P(B) = $\frac{3}{5}$ P(A/B) = $\frac{1}{2}$ and P(A ∪ B) = $\frac{4}{5}$ then P(A) =
- $\frac{3}{10}$
- $\frac{1}{2}$
- $\frac{1}{5}$
- $\frac{3}{5}$
View Solution
4.
A bag contains 2n + 1 coins. It is known that n of these coins have head on both sides whereas the other n + 1 coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is $\frac{31}{42}$, then the value of n is
- 8
- 5
- 10
- 6
View Solution
5.
In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is
- $\frac{7}{12}$
- $\frac{5}{36}$
- $\frac{5}{12}$
- $\frac{7}{36}$
View Solution
6.
If A and B are two events such that P(A) = $\frac{1}{3}$, P(B) = $\frac{1}{2}$ and P(A ∩ B) = $\frac{1}{6}$, then P(A'/B) is
- $\frac{2}{3}$
- $\frac{1}{3}$
- $\frac{1}{2}$
- $\frac{1}{12}$
View Solution
7.
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is
- $\frac{1}{18}$
- $\frac{5}{18}$
- $\frac{1}{5}$
- $\frac{2}{5}$
View Solution
8.
If A and B are events such that P(A)=$\frac{1}{4}$, P(A/B)=$\frac{1}{2}$ and P(B/A)=$\frac{2}{3}$ then P(B) is
- $\frac{2}{3}$
- $\frac{1}{6}$
- $\frac{1}{2}$
- $\frac{1}{3}$
View Solution
9.
Events E₁ and E₂ form a partition of the sample space S. A is any event that P(E₁) = P(E₂) = $\frac{1}{2}$, P(E₂/A) = $\frac{1}{2}$ and P(A/E₂) = $\frac{2}{3}$, then P(E₁/A) is
- $\frac{1}{2}$
- $\frac{2}{3}$
- 1
- $\frac{1}{4}$
View Solution
10.
A die is thrown four times. The probability of getting perfect square in at least one throw is
- $\frac{16}{81}$
- $\frac{65}{81}$
- $\frac{23}{81}$
- $\frac{58}{81}$
View Solution

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KCET PYQs for Conditional Probability with Solutions: Practice KCET Previous Year Questions

KCET PYQs for Conditional Probability with Solutions

2.
If A and B are the two events such that \(P(A) = \frac{1}{2}\), \(P(B) = \frac{1}{3}\) and \(P(A|B) = \frac{1}{4}\), then \(P(A' \cap B')\) is

3.
Given that A and B are two events such that P(B) = \(\frac{3}{5}\) P(A/B) = \(\frac{1}{2}\) and P(A ∪ B) = \(\frac{4}{5}\) then P(A) =

4.
A bag contains 2n + 1 coins. It is known that n of these coins have head on both sides whereas the other n + 1 coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is \(\frac{31}{42}\), then the value of n is

5.
In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is

6.
If A and B are two events such that P(A) = \(\frac{1}{3}\), P(B) = \(\frac{1}{2}\) and P(A ∩ B) = \(\frac{1}{6}\), then P(A'/B) is

7.
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is

8.
If A and B are events such that P(A)=\(\frac{1}{4}\), P(A/B)=\(\frac{1}{2}\) and P(B/A)=\(\frac{2}{3}\) then P(B) is

9.
Events E₁ and E₂ form a partition of the sample space S. A is any event that P(E₁) = P(E₂) = \(\frac{1}{2}\), P(E₂/A) = \(\frac{1}{2}\) and P(A/E₂) = \(\frac{2}{3}\), then P(E₁/A) is

10.
A die is thrown four times. The probability of getting perfect square in at least one throw is

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KCET PYQs for Conditional Probability with Solutions

2.If A and B are the two events such that \(P(A) = \frac{1}{2}\), \(P(B) = \frac{1}{3}\) and \(P(A|B) = \frac{1}{4}\), then \(P(A' \cap B')\) is

3.Given that A and B are two events such that P(B) = \(\frac{3}{5}\) P(A/B) = \(\frac{1}{2}\) and P(A ∪ B) = \(\frac{4}{5}\) then P(A) =

4.A bag contains 2n + 1 coins. It is known that n of these coins have head on both sides whereas the other n + 1 coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is \(\frac{31}{42}\), then the value of n is

5.In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is

6.If A and B are two events such that P(A) = \(\frac{1}{3}\), P(B) = \(\frac{1}{2}\) and P(A ∩ B) = \(\frac{1}{6}\), then P(A'/B) is

7.Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is

8.If A and B are events such that P(A)=\(\frac{1}{4}\), P(A/B)=\(\frac{1}{2}\) and P(B/A)=\(\frac{2}{3}\) then P(B) is

9.Events E1 and E2 form a partition of the sample space S. A is any event that P(E1) = P(E2) = \(\frac{1}{2}\), P(E2/A) = \(\frac{1}{2}\) and P(A/E2) = \(\frac{2}{3}\), then P(E1/A) is

10.A die is thrown four times. The probability of getting perfect square in at least one throw is

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2.
If A and B are the two events such that \(P(A) = \frac{1}{2}\), \(P(B) = \frac{1}{3}\) and \(P(A|B) = \frac{1}{4}\), then \(P(A' \cap B')\) is

3.
Given that A and B are two events such that P(B) = \(\frac{3}{5}\) P(A/B) = \(\frac{1}{2}\) and P(A ∪ B) = \(\frac{4}{5}\) then P(A) =

4.
A bag contains 2n + 1 coins. It is known that n of these coins have head on both sides whereas the other n + 1 coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is \(\frac{31}{42}\), then the value of n is

5.
In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is

6.
If A and B are two events such that P(A) = \(\frac{1}{3}\), P(B) = \(\frac{1}{2}\) and P(A ∩ B) = \(\frac{1}{6}\), then P(A'/B) is

7.
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is

8.
If A and B are events such that P(A)=\(\frac{1}{4}\), P(A/B)=\(\frac{1}{2}\) and P(B/A)=\(\frac{2}{3}\) then P(B) is

9.
Events E₁ and E₂ form a partition of the sample space S. A is any event that P(E₁) = P(E₂) = \(\frac{1}{2}\), P(E₂/A) = \(\frac{1}{2}\) and P(A/E₂) = \(\frac{2}{3}\), then P(E₁/A) is

10.
A die is thrown four times. The probability of getting perfect square in at least one throw is