What is the probability of selecting a white die on the second draw, given that the first die picked was black...A box has black and white dice. Two dies are picked without replacement. The...

What is the probability of selecting a white die on the second draw, given that the first die picked was black...

A box has black and white dice. Two dies are picked without replacement. The probability of selecting a black die and then a white die is 0.34, and the probability of selecting a black die first is 0.47.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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This questions involves conditional probability.

For two events A and B, the probability of B taking place if A has already taken place P(B|A) and the probability of both A and B taking place P(A and B) is related by:

P(B|A) = `(P(A and B))/(P(A))`

Here the probability of picking a black die and then a white die is P(A and B) = 0.34. The probability of picking a black die first is P(A) = 0.47.

This gives the probability that a white die is picked after a black die has already been picked P(B|A) = `(0.34)/(0.47) ~~ 0.72`

There is a 0.72 probability that a white die is picked if a black die has already been picked.

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