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# Find the mean of the distribution

The number two is both even and prime. Suppose a card with a two is mixed with seven other even number cards that are not twos. A pair of cards is drawn with replacement.

I understand how to get the number of different samples possible and that is 64.

I understand how to get the number of samples for which the proportion of non-prime even numbers is one and that is 49.

I do not understand how I find the mean of the sampling distribution of the proportion of non-prime even numbers. Although I know the answer is 0.875 I do not understand how you arrive at that. Can you please show me how that is determined?

#### Solution Preview

There are 8 total cards; one is prime, seven are not prime. You are correct that the number of different possible of pairs of cards is 64 (8 possibilities for card #1, 8 for card #2, 8 x 8 = 64). Similarly there are 49 possible pairs of non-prime cards (7 x 7 = 49).

You want to find the mean of the sampling distribution of the proportion of non-prime cards. For each pair of cards, the proportion ...

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