Question 31 - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Question 31 Two students Mehul and Rashi are seeking admission in a college. The probability that Mehul is selected is 0.4 and the probability of selection of exactly one of the them is 0.5 . Chances of selection of them is independent of each other. Find the chances of selection of Rashi. Also find the probability of selection of at least one of them.Let the events be A: Mehul is selected B: Rashi is selected Given that Probability Mehul is selected = 0.4 𝑃(𝐴) = 0.4 Also, the probability of selection of exactly one of the them is 0.5 P(Mehul selected, but Rashi not selected) + P(Rashi l selected, but Mehul not selected) = 0.5 𝑃(𝑨∩𝑩 ̅) + 𝑃(𝑩∩𝑨 ̅) = 0.5 Given that events are independent, so we can write 𝑃(𝐴∩𝐵 ̅) = P(A) × P(𝑩 ̅) 𝑃(𝐵∩𝐴 ̅) = P(B) × P(𝑨 ̅) Now, our equation (1) becomes 𝑃(𝐴∩𝐵 ̅) + 𝑃(𝐵∩𝐴 ̅) = 0.5 P(A) × P(𝑩 ̅) + P(B) × P(𝑨 ̅) = 0.5 Using complement formula P(A) × (1 – P(B)) + P(B) × (1 – P(A)) = 0.5 Putting P(A) = 0.4 0.4 × (1 – P(B)) + P(B) × (1 – 0.4) = 0.5 0.4 – 0.4 × P(B) + P(B) × 0.6 = 0.5 P(B) × 0.6 – P(B) × 0.4 = 0.5 – 0.4 P(B) × (0.6 – 0.4) = 0.1 P(B) × 0.2 = 0.1 P(B) × 2/10 = 1/10 P(B) = 1/10 ×10/2 P(B) = 1/2 P(B) = 0.5 Thus, chances of selection of Rashi is 0.5 We also need to find Probability of selecting atleast one of them Probability of selecting atleast one of them Probability of selecting atleast one of them = P(A ∪ B) = P(A) + P(B) – P(A ∩ B) Since events are independent, P(A ∩ B) = P(A) × P(B) = P(A) + P(B) – P(A) × P(B) Putting values = 0.4 + 0.5 – 0.4 × 0.5 = 0.9 – 0.2 = 0.7