Probability

Question

A building contractor buys 60?% of his cement from supplier A and 40?% from supplier B. A total of 75?% of the bags from A arrive? undamaged, while 90?% of the bags from B arrive undamaged. Find the probability that a damaged bag is from supplier B.

Answer 1

I like doing this with a simple tree diagram rather than conditional probability.

 P( from A and good ) = .6 * .75 = .45

 p(A and damaged) = .6*.25 = .15

P(B and good) = .4*.9 = .36

P(B and damaged)= .4*.1 = .04.

 

So the probability it comes damaged in the first place from either company is .19.

 

The probability that the damaged thing came from B is .04/,19 = .2105 or 21.05% of the damaged goods come from company B.

 

Hope this helped