A blue box has3 apples and 1 banana in it, and a red box has 5 apples and 6banan

Question

A blue box has3 apples and 1 banana in it, and a red box has 5 apples and 6bananas in it. The apples in the blue box have the probability 1/3of being green and the probability 2/3 of being red. The apples inthe red box are green with probability 1/4 and red with probability3/4. If we pick randomly one of the boxes, and then one of thefruits in that box, find thefollowing:

(a) Theprobability that a red apple from the blue box isselected.

(b) Theprobability that an apple is selected.

(c) Theprobability that the box was blue, given that an apple wasselected.

(d) The probability that thebox was red, given that a red apple was selected.

Explanation / Answer

(a) Theprobability that a red apple from the blue box isselected.

Just take theprobability of picking the blue box, then the probability ofpicking an apple, then the probability that its red and multiply ittogether.

1/2 x 3/4 x 2/3= 1/4

(b) Theprobability that an apple is selected.

Take the totalnumber of apples and divided it by the total number offruits

8/15

(c) Theprobability that the box was blue, given that an apple wasselected.

1/2 x 3/4 =3/8

(d) The probability that thebox was red, given that a red apple was selected.

3/4 x 5/11 x 3/4 =45/176

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