There are two treasure chests filled with gemstones. Treasure chest A contains: 6 rubies, 9 emeralds,...
There are two treasure chests filled with gemstones. Treasure
chest A contains: 6
rubies, 9 emeralds, and 5 diamonds. Treasure chest B contains: 3
rubies, 7 emeralds,
and 10 diamonds. A diamond is selected from one of the chests at
random. What is the
probability that the diamond was selected from Treasure chest
A?
Homework Answers
Solution:
Contingency table can be written as follows
|
Treasure Chests |
Rubies |
Emeralds |
Diamonds |
|
|
A |
6 |
9 |
5 |
20 |
|
B |
2 |
7 |
10 |
19 |
|
8 |
16 |
15 |
39 |
We need to find
P(Chest A | Diamond) here we will use conditional probability
P(Chest A| Diamond) = P(ChestA and Diamond)/ P(Diamond) = (5/39) /
(15/39) = 5/15 = 0.33
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