Chapter 7.2, Problem 9E

Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows:

$\begin{array}{cccccc}y& 0& 1& 2& 3& 4\\ p(y)& .65& .20& .10& .04& ?\end{array}$

a. Only y values of 0, 1, 2, 3, and 4 have positive probabilities. What is p(4)? (Hint: Consider the properties of a discrete probability distribution.)

b. How would you interpret p(1) =.20?

c. Calculate P(y ≤ 2), the probability that the carton contains at most two broken eggs, and interpret this probability.

d. Calculate P(y ≤ 2), the probability that the carton contains fewer than two broken eggs. Why is this smaller than the probability in Part (c)?

e. What is the probability that the carton contains exactly 10 unbroken eggs?

f. What is the probability that at least 10 eggs are unbroken?