6. Conditional Probability Formulas
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How many red marbles are there in the jar? How many of them are large?
5/7
We are told that a jar contains 10 large red marbles, 4 small red marbles, 6 large blue marbles, and 5 small blue marbles. We want to know the conditional probability of choosing a large marble given that it is red. To do that we will use the Conditional Probability Formula.
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Conditional Probability Formula |
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For any two events A and B, the probability of B occuring, given that event A has occured, is P(B|A)=P(A andB)/P(A), where P(A) ≠0. |
Let's start with identifying the probabilities.
| Identifying the Probabilities |
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| P(B|A) = P(large marble, given that it is red) |
| P(A)=P(red marble)=10+4=14 |
| P(A andB)=P(large red marble)=10 |
Now let's find P(B|A). P(B|A)=P(A andB)/P(A)=10/14=5/7