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Question:

The probability of the drawn ball from U₂ being white is?

23/30

19/30

13/30

11/30

Solution:

P(W) = P(H, W) + P(T, W)
If head comes then W or R from U₁ and U₂ will contain 2W or 1W1R
P(H, W) = 1/2 (3/5 × 1 + 2/5 × 1/2) = 2/5
If tail comes, then WW or RR or WR from U₁ and U₂ will contain 3W or 1W2R or 2W1R
P(T, W) = 1/2 (3/10 × 1 + 1/10 × 1/3 + 6/10 × 2/3) = 11/30
P(W) = 2/5 + 11/30 = 23/30