A box contains 6 white balls and 4 black balls. Balls are drawn from the box without replacement until either a white ball is drawn or 3 balls have been drawn. Find the expected number of balls that will be drawn from the box.
2026-04-03 02:57:53.1775185073
Expectation of the number balls are drawn
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Hint. If only one ball is drawn, it must be white. The probability that this happens is $$p_1=\frac6{10}\ .$$ If two balls are drawn they must be... then... so the probability is $$p_2=\cdots\ .$$ See if you can fill in the gaps, then find the probability that $3$ balls are drawn, $4$ balls etc. Then the expectation is $$1p_1+2p_2+\cdots\ .$$ Good luck!