Question

A carton contains 12 eggs. A particular carton is known to have 4 cracked eggs. An...

A carton contains 12 eggs. A particular carton is known to have 4 cracked eggs. An inspector randomly chooses 6 eggs from this carton for inspection. Let X be the number of cracked eggs in the 6 chosen for inspection.

a. What is the probability that there is at least 1 cracked egg chosen by the inspector?

b. What is the probability that there is exactly 1 cracked egg chosen by the inspector?

c. What is the probability that there are no cracked eggs chosen by the inspector?

d. What is the probability that there are at most 2 cracked eggs chosen by the inspector?

e. Find the expected value of X.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Here X has hypergeometric distribution with parameters as follow:

Population size: N = 12

Number of eggs selected: n = 6

Number of cracked eggs: k =4

(a)

The probability that there is at least 1 cracked egg chosen by the inspector is

(b)

The probability that there is exactly 1 cracked egg chosen by the inspector is

(c)

The probability that there are no cracked eggs chosen by the inspector is

(d)

The probability that there are at most 2 cracked eggs chosen by the inspector is

(e)

The expected value of X is

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