Question

There are two boxes. Box I contains 4 Red and 3 white balls. Box II contains 5 red and 2 white balls. Two balls are transferred from Box I to Box II. One ball is then drawn from box II randomly. What is the probability for that ball to be red? ​

Answer 1

Answer:

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Example:

Explanation:

Box I → 4R, 3W i.e. total = 7

Box II → 5R, 2W i.e. total = 7

Let A = both balls from box I are R

B = 1 ball is R and I is W from box I

C = both balls are W from box I

D = 1 ball is R from box II

∴ Probability for red ball R = P(D) and

P(D) = P(A) ∙ P(D/A) + P(B) ∙ P(D/B) + P(C) ∙ P(D/C)

= [(4C2)/(7C2)](7/9) + [(3C2)/(7C2)](5/9) + [(4 × 3)/(7C2)](6/9)

= [(6/21) × (7/9)] + [(3/21) × (5/9)] + [(12/21) × (6/9)]

= [(42 + 15 + 72)/189]

= (129/189)

= (43/63).