When eggs are packed in boxes the probability than an egg is

\"When eggs are packed in boxes the probability than an egg is broken is 0.008. Calculate the probability that in a consignment of 500 eggs fewer than 4 eggs are broken\".

Solution

\"There are 5000 students in a university. Calculate the probability that exactly 15 of them have their birthdays on January 1st by using a suitable Poisson approximation - how do I actually make a \"suitable\" Poisson approximation?

Let lambda = 5000/365 = approx 13.7 students have a birthday on each day including Jan 1

P(X = 15) = e^-13.7 (13.7^15) / 15! = 0.0965

\"When eggs are packed in boxes the probability than an egg is broken is 0.008. Calculate the probability that in a consignment of 500 eggs fewer than 4 eggs are broken\".

Lambda = 0.008 x 500 = 40 eggs

P(X < 4) = sum x from 0 to 3: e^-40 (40^x) / x! = 0.434