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COMEDK · Maths · 36. Probability

Bag A contains 3 white and 2 red balls. Bag B contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from bag A and put into bag B. However if tail appears then 2 balls are drawn at random from bag A and put into bag B. Now one ball is drawn at random from bag B. Given that the drawn ball from B is white, the probability that head appeared on the coin is

  1. A \(\dfrac{19}{30}\)
  2. B \(\dfrac{12}{23}\)
  3. C \(\dfrac{11}{23}\)
  4. D \(\dfrac{23}{30}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\dfrac{12}{23}\)

Step-by-step Solution

Detailed explanation

\(P(H) = P(T) = \dfrac{1}{2}\) If Head: 1 ball drawn from Bag A (3W, 2R), put into Bag B (1W). \(P(W_B|H) = \dfrac{3}{5} \times 1 + \dfrac{2}{5} \times \dfrac{1}{2} = \dfrac{3}{5} + \dfrac{1}{5} = \dfrac{4}{5}\) If Tail: 2 balls drawn from Bag A, put into Bag B (1W).…