help probability problem
c) The manager of a new supermarket chain in Petting Jaya guarantees that none of his cartons each containing 10 eggs will contain more than one cracked egg. If a carton contains more than one cracked egg, he will replace the whole carton and will allow the customer to buy the next carton at half the price. The probability that an individual egg is cracked is 0.02. i) Show the probability that the manager will have to replace a given canon of eggs is 0.016 accurate to 3 decimal places. ii) Using the Poisson approximation to the Binomial distribution, find the probability that the number of cartons replaced is less than 2 in a consignment of 200 cartons.
Claim none of his cartons of 10 eggs will contain more than one cracked egg.
Prob that the manager will have to replace a given carton of eggs = P(cracked eggs>1 in 10 cartons)
X = no of cracked eggs follow a Binomial with p =0.02 and q =0.98
n =10 here
Hence binomial prob for P(x>1) = 1-P(x=0)-P(X=1) = 1-(0.02)10-(0.02)9(0.98)
=0.0161776
= 0.016 (upto 3 decimal places.)
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