Black and blue balls -T'IS probability

Probability Level 2

A box contains 24 balls of which 12 are black and 12 are white. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4 th 4^\text{th} time on the 7 th 7^\text{th} draw is:

5 64 \dfrac5{64} 27 32 \dfrac{27}{32} 11 32 \dfrac{11}{32} 5 32 \dfrac5{32}

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2 solutions

Required probability=Probability of drawing 3 W and 3 B balls in 6 draws and drawing a white ball in 7th draw which is 6 C 3 ( 12 / 24 ) 3 ( 12 / 24 ) 3 ( 12 / 24 ) 6C3(12/24)^3(12/24)^3(12/24)

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Shyam Kumar
Dec 28, 2015

Use binomial theorem: 6C3 (1/2)^3 *( 1/2)^3 multiplied by 1/2 for the 7th pick

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