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Question

A bag contains 3 white, 3 black, and 2 red balls. One by one three balls are drawn without replacing them, then find the probability that the third ball is red.

A
14
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B
34
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C
13
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D
None of these
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Solution

The correct option is B 14
Let R stand for drawing red ball, B for black ball, and W for drawing white ball. Then, the required probability =P(WWR)+P(BBR)+P(WBR)+P(BWR)+P(WRR)+P(BRR)+P(RWR)+P(RBR)
=3×2×28×7×6+3×2×28×7×6+3×3×28×7×6+3×3×28×7×6+3×2×18×7×6+3×2×18×7×6+2×3×18×7×6+2×3×18×7×6

=256+256+356+356+156+156+156+156 =14

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