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Question

A bag contains 5 white, 7 red and 3 black balls. If three balls are drawn one by one without replacement, find the probability that none is red.

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Solution

Consider the given events.
A = A white or black ball in the first draw
B = A white or black ball in the second draw
C = A white or black ball in the third draw

Now, PA=815PB/A=714=12PC/AB=613 Required probability = PABC =PA×PB/A×PC/AB =815×12×613 =865

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