<p>A bag contains 5 white and 3 black balls. 4 balls are successively drawn out and not replaced. What is the probability that they are alternately of different colours?</p>
Step-by-Step Solution
Key Concept: Alternately different colors means we need either WBWB or BWBW sequence. Calculate probability for each sequence using conditional probability without replacement, then add them.
<p><strong>Step 1:</strong> Identify possible alternating sequences with 4 draws from 5 white and 3 black balls: either WBWB or BWBW.</p><p><strong>Step 2:</strong> Calculate P(WBWB):<br/>P(W)·P(B|W)·P(W|WB)·P(B|WBW) = (5/8)·(3/7)·(4/6)·(2/5) = 120/1680 = 1/14</p><p><strong>Step 3:</strong> Calculate P(BWBW):<br/>P(B)·P(W|B)·P(B|BW)·P(W|BWB) = (3/8)·(5/7)·(2/6)·(4/5) = 120/1680 = 1/14</p><p><strong>Step 4:</strong> Total probability = P(WBWB) + P(BWBW) = 1/14 + 1/14 = 2/14 = <strong>1/7</strong></p><p>∴ Answer: A</p>
Correct Answer: A