A fruit store obtains its supply of apples from three producers, X, Y and Z. Producer X supplies 20% of the requirements and on the average 2% of his apples are bruised. Producers Y and Z supply 30 and 50%, respectively. On the average 1% of Y’ s and 5% of Z fs apples are bruised. In a given week the fruit store owner purchases 5000 apples. If an apple chosen at random turns out to be bruised, what is the probability that it was supplied by Y ?
X supplies 20% of the requirements and
on average 2% of his apples are bruised.
Y supply 30% and Z supply 50%. On average, 1% of Y's and 5% of Z is apples are bruised.
Hre total apples purchased = 5000
Total from producer X = 5000 * 0.2 = 1000
Total bruised apples of producer X = 1000 * 0.02 = 20
Total from producer Y = 5000 * 0.3 = 1500
Total bruised apples of producer Y = 1500 * 0.01 = 15
Total from producer Z = 5000 * 0.5 = 2500
Total bruised apples of producer Z = 2500 * 0.05 = 125
Total bruised apple = 20 + 15 + 125 = 160
Probability that it was supplied by Y = Total bruised apples of producer Y/ Total bruised apples = 15/160 = 0.09375
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