## Related questions with answers

Question

A building contractor buys 70% of his cement from supplier A and 30% from supplier B. A total of 90% of the bags from A arrive undamaged , while 95% of the bags from B arrive undamaged . Give the probabilities that a damaged bag is from the following sources.

Supplier B

Solution

VerifiedStep 1

1 of 3Apply Bayes' Theorem (special case)

$P(F|E)=\frac{P(F)\cdot P(E|F)}{P(F)\cdot P(E|F)+P(F^{\prime})\cdot P(E|F^{\prime})}$

First, draw a tree digram with the given information.

Probabilities written in black are given, and the red ones are their corresponding complements.

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