# Probability and Statistics Question?

From a box containing 5 dimes and 2 nickels, three coins are selected at random without replacement. Find the probability distribution for the total T of the 3 coins. Express the probability distribution graphically as a probability histogram.

Relevance

There are 3 cases to consider:

2 nickels + 1 dime (20¢)

1 nickel + 2 dimes (25¢)

0 nickels + 3 dimes (30¢)

The ways to get each of the cases would be:

20¢ --> C(2,2) * C(5,1) = 5 ways

25¢ --> C(2,1) * C(5,2) = 20 ways

30¢ --> C(2,0) * C(5,3) = 10 ways

That's out of a total of 35 ways which we can find by adding or calculating C(7,3) = 35.

Thus the respective probabilities are:

T --> P(T)

20¢ --> 5/35 = 1/7

25¢ --> 20/35 = 4/7

30¢ --> 10/35 = 2/7

Draw a histogram to match (something like this, but vertically):

20¢ : @

25¢ : @@@@

30¢ : @@

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• prob of selecting 3 dimes is (5C3)(2C0) / (7C3) = 10/35=2/7. T=30 (cents)

prob of selecting 2 dimes and 1 nickel is (5C2)(2C1) / (7C3) = 20/35=4/7. T=25.

prob of selecting 1 dime and 2 nickels is (5C1)(2C2) / (7C3) = 5/35=1/7. T=20.

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