CBSE Class 12 Mathematics — Probability

Assertion (A): In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is $\frac{2}{3}$. Reason (R): For any two events A and B, $P(A|B) = \frac{P(A \cap B)}{P(B)}$.

(a) Out of two bags, bag I contains 3 red and 4 white balls and bag II contains 8 red and 6 white balls. A die is thrown. If it shows a number less than 3 then a ball is drawn at random from bag I, otherwise a ball is drawn at random from bag II. Find the probability that the ball drawn from one of the bags is a red ball. OR (b) The probability of simultaneous occurrence of at least one of the two events X and Y is a. If the probability that exactly one of the events X, Y occurs is b, prove that $P(X') + P(Y') = 2 - 2a + b$.

What are the possible amounts, the person can win?

(a) What is the probability that the person wins atleast Rs 2,00,000? OR (b) What is the probability that the person does not win any amount?

In another jackpot, Rohan also bought a ticket having a prize money of Rs 5,00,000. The chances of winning the jackpot are 1 in 1,00,000. Find the probability that on exactly one of tickets he wins the jackpot.