A bag contains 6R and 4W balls. 4 balls are drawn one by one without replacement and were found to be at least 2 white. Find the probability that next draw will give a white ball.
Answer is 34/115
Probability-I think this one is based on total probability therorem, is it?
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0Yes, the answer is 34/115. – 2017-02-16
1 Answers
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Indeed, applying the law of total probability is the first step.
Let $F$ be the event that the fifth ball drawn is white, and $W$ the count of white balls among the first four drawn. Then : $$\mathsf P(F\mid W\geq 2) ~=~ \sum\limits_{w=2}^4 \mathsf P(F\mid W=w)~\mathsf P(W=w\mid W\geq 2)$$