Question

A building contractor buys 7070​% of his cement from supplier A and 3030​% from supplier B. A total of 9595​% of the bags from A arrive​ undamaged, while 7070​% of the bags from B arrive undamaged. Find the probability that anan undamagedundamaged bag is from supplier Upper AA.

Answer 1

Title:

The answer is $\frac{133}{174}$.

Step-by-step explanation:

Let the building contractor bought 1000 cement in total.

70% of 1000 = 700 cements were from A and (1000 - 700) = 300 cements were from B.

The number of undamaged bag from A was 95% of 700 = $\frac{95}{100} \times700 = 7\times95 = 665$ and the number of undamaged bags from B was 70% of 300 = $\frac{70}{100} \times300 = 210$.

Total undamaged bags were (665 + 210) = 870.

The probability that an undamaged bag is from A is $\frac{665}{870} = \frac{133}{174}$.