Odalys sells eggs to restaurants. Before she sends a package of eggs to a custom
ID: 2942919 • Letter: O
Question
Odalys sells eggs to restaurants. Before she sends a package of eggs to a customer, she selects five of the eggs in the package at random and checks to see if they are spoiled. She won't send the package if any of the eggs she tests are spailed. Suppose the package contain 18 eggs, and half of them are spoiled. How likely is it that. Odalys detects a spoiled egg? Suppose that a package contains 144 eggs, and half of them are spoiled. How likely is it that. Odalys detects a spoiled egg? Suppose that a package contains 144 eggs, and 10 of them are spoiled. How likely is it that Odalys detocts a spoiled egg? What seems to have a bigger effect on the probability of finding a spoiled egg: the size of the package or the percentage of spoiled eggs? Justify your answer.Explanation / Answer
(a) The probability that she detects one of the nine spoiled eggs is 1 - prob that the five she selects for inspection are all good eggs. The probability is one minus the number of ways she can select five good eggs over the number of ways she can pick five eggs. 1 - (9*8*7*6*5)/(18*17*16*15*14) = 0.985294118 So, there is a 98.5% chance she will detect a spoiled egg. (b) If there are 144 eggs and 72 spoiled ones, the probability is one minus the number of ways she can selected five good eggs over the number of ways she can pick five eggs. 1- 72*71*70*69*68/144*143*142*141*140 = 0.968308287 So, there is a 96.8% chance that she will detect a spoiled egg; still pretty high. (c) If there are 144 eggs and 10 spoiled ones, the probability is one minus the number of ways she can selected five good eggs over the number of ways she can pick five eggs. 1- 134*133*132*131*130/144*143*142*141*140 = 0.305917657 So, there is only a 30.6% chance that she will find one of the spoiled eggs. (d) The percent of spoiled eggs seems more important than the size of the package. When we kept the percentage the same and made the package 8x bigger, the detection percentage only went from 98.5 down to 96.8, but when we made the spoiled eggs 7.2x smaller, we went down to 30.6% chance that we would detect a bad egg.
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