Question
A coin is tossed. If head occurs, a ball is drawn from a
bag containing 3 red and 4 green balls. If tail occurs, a die is thrown. The probability that the final outcome is a green ball or a prime number is:Solution
Coin toss outcomes: – P(Head) = 1/2 – P(Tail) = 1/2 If head occurs: – Bag contains 3 red and 4 green balls → total = 7 – P(Green | Head) = 4/7 – P(Green ball) = (1/2) × (4/7) = 2/7 If tail occurs: – A die is thrown – Prime outcomes = {2, 3, 5} → 3 favourable out of 6 – P(Prime | Tail) = 3/6 = 1/2 – P(Prime number) = (1/2) × (1/2) = 1/4 Since both cases are mutually exclusive, total probability = 2/7 + 1/4 = (8 + 7)/28 = 15/28
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