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.
Puzzling
Favorite Answer
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¢ : @@
Leonard
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.
This is your prob dist:
T P(T)
30 2/7
25 4/7
20 1/7