SOLUTION: Suppose that you have a barrel with 5 apples and 8 oranges in it. If 3 fruits are selected, what is the probability you select exactly 2 apples?

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose that you have a barrel with 5 apples and 8 oranges in it. If 3 fruits are selected, what is the probability you select exactly 2 apples?      Log On


   

Question 1190900: Suppose that you have a barrel with 5 apples and 8 oranges in it. If 3 fruits are selected, what is the probability you select exactly 2 apples?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Solving by an elementary method -- which is useful for gaining an understanding of basic probability....

P(apple,apple,orange) = %285%2F13%29%284%2F12%29%288%2F11%29+=+160%2F1716
P(apple,orange,apple) = %285%2F13%29%288%2F12%29%284%2F11%29+=+160%2F1716
P(orange,apple,apple) = %288%2F13%29%285%2F12%29%284%2F11%29+=+160%2F1716

P(2 apples and 1 orange) = 480%2F1716+=+40%2F143

(2) Solving by a more sophisticated method of combinatorics....

The good outcomes are when you choose 2 of the 5 apples and 1 of the 8 oranges; the total number of possibilities is when you choose any 3 of the 13 fruits.

P(2 apples and 1 orange) = %28C%285%2C2%29%2AC%288%2C1%29%29%2FC%2813%2C3%29+=+%2810%2A8%29%2F286+=+80%2F286+=+40%2F143