Question

Three poultry farms B1, B2, and B3 supply chicken eggs to the same local market. The market performs some quality testing on the supplied eggs. It has been observed that 80% of eggs supplied by B1 are acceptable. 90% eggs of Farm B2 are acceptable and only 60% eggs of farm B3 is acceptable. Each week, farm B1 supplies 3000 eggs, B2 supplies 4000 eggs and B3 supplies 3000 eggs. All of the eggs are put together at random in one bin and packed for sale by the local market. a) What is the probability that an egg come from Farm B1 or B2? b) What is the probability that the market received an egg that is acceptable?

Answer 1

Answer:

a. 0.58

b. 0.78

Step-by-step explanation:

a. The probability of egg come from B1 or B2

P(B1) = 3000/10000 = 0.3

P(B2) = 4000/10000 = 0.4

P(P1 ∪ B2) = 0.3 + 0.4 -(0.3)(0.4)

P(P1 ∪ B2) = 0.7 - 0.12

P(P1 ∪ B2) = 0.58

b. The probability that the market received an egg that is acceptable

P(received an egg that is acceptable) = P(B1 acceptable) + P(B2 acceptable) + P(B3 acceptable)

P(received an egg that is acceptable) = 0.80*3000 + 0.90*4000 + 0.60*3000 / 10000

P(received an egg that is acceptable) = 2400 + 3600 + 1800 / 10000

P(received an egg that is acceptable) = 7800 / 10000

P(received an egg that is acceptable) = 0.78