Crate #1 contains 3 apples, 4 oranges, and 2 pears. Crate #2 contains 5 apples and 3 pears. Julia wants a piece of fruit and to select it she will roll a fair die, selecting a random fruit from Crate #1 if the die shows a 3 or 4 and otherwise selecting it from Crate #2. (a) Find the probability that the selected fruit is a pear. (b) Given that the selected fruit is a pear, find the probability that it came from Crate #1.

Crate #1 contains 3 apples, 4 oranges, and 2 pears. Crate #2 contains 5 apples and 3 pears. Julia wants a piece of fruit and to select it she will roll a fair die, selecting a random fruit from Crate #1 if the die shows a 3 or 4 and otherwise selecting it from Crate #2. (a) Find the probability that the selected fruit is a pear. (b) Given that the selected fruit is a pear, find the probability that it came from Crate #1.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Crate #1 contains 3 apples, 4 oranges, and 2 pears. Crate #2 contains 5 apples and
3 pears. Julia wants a piece of fruit and to select it she will roll a fair die, selecting
a random fruit from Crate #1 if the die shows a 3 or 4 and otherwise selecting it
from Crate #2.
(a) Find the probability that the selected fruit is a pear.
(b) Given that the selected fruit is a pear, find the probability that it came from
Crate #1.

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Step 3: General calculations

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Step 4: a) Probability that the selected fruit is a pear

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Step 5: b) Probability of crate 1 given that selected fruit is pear

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