Homework SourseCrates of eggs are inspected for blood clots by randomly sel
Crates of eggs are inspected for blood clots by randomly selecting 5 eggs from the crate without replacement and examining their contents. Let Y be the number of eggs containing blood clots out of the 5 inspected.
1. The crate contains 40 eggs, of which 4 have blood clots, what is the probability at most two of the 5 eggs inspected will contain blood clots?
Crates of eggs are inspected for blood clots by randomly selecting 5 eggs from the crate without replacement and examining their contents. Let Y be the number of eggs containing blood clots out of the 5 inspected.
1. The crate contains 40 eggs, of which 4 have blood clots, what is the probability at most two of the 5 eggs inspected will contain blood clots?
1. The crate contains 40 eggs, of which 4 have blood clots, what is the probability at most two of the 5 eggs inspected will contain blood clots?
Solution
1. Here Y is the number of eggs containing blood clots out of the 5 eggs inspected.
Now out of 40 eggs 4 have blood clots.
now we need to find the probability that at most two of the 5 eggs inspected will contain blood clots.
i.e, we need to find P[X<=2]=P[Y=0]+P[Y=1]+P[Y=2]
now Y~hypergeometric(40,4,5)
so pmf of Y is f(y)=(4Cy*40-4C5-y)/40C5 y=0,1,2,3,4,5
so P[at most two of 5 eggs will contain blood clots will be]=P[Y=0]+P[Y=1]+P[Y=2]=0.572929+0.358081+0.065106=0.996116 [answer]
