just need help with 7 please show work and im pretty sure you use hypergeometric

Question

just need help with 7 please show work and im pretty sure you use hypergeometric distribution because that how i did six

6. Four eggs are chosen one at a time and without replacement from a carton containing 12 white eggs of which 3 are cracked.

    a)   Compute the probability that 2 of the 4 are cracked.

Compute the probability that at least 1 of the 4 is cracked.

Answer the previous 2 parts assuming the sampling is one at a time with replacement.

7. Suppose that the carton of eggs described in the previous exercise also contains 6 brown eggs of which 1 is cracked, giving a total of 18eggs. Four eggs are chosen one at a time without replacement from the carton.

Compute the probability that 1 brown cracked egg and 2 white cracked eggs are selected.

Compute the probability that at least 1 cracked egg is selected.

  Answer parts a) and b) assuming the sampling is one at a time with replacement.

Explanation / Answer

7:

Total number of eggs: 18

Number of ways of selecting 4 eggs out of 18 is C(18,4)= 3060.

Out of 18 eggs, 3+1=4 are cracked and 14 are good.

So number of ways selecting 1 brown cracked egg, 2 white cracked egg and 1 good egg is

C(1,1)C(3,2)C(14,1) = 42

So the probability that 1 brown cracked egg and 2 white cracked eggs are selected is

42 / 3060 = 0.0137

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The probability that no egg is cracked out of 4 is

C(14, 4) / C(18,4) = 1001 /3060

So the probability that at least 1 cracked egg is selected is

1 - 1001 /3060 = 0.6729

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