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Suppose a microprocessor is chosen at random from a collection of 100. Assume 20 are Intels and 80 are AMDs. Also assume that 10 of the Intels are 2.0 GHz. What is the probability that the selected microprocessor is 2.0 GHz given that it is an Intel?

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There are twenty intel chips and ten are 2 GHz. The choice is random, so there is a 1/2 probability of choosing a 2 GHz chip.

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Hint: What proportion of the Intels are 2.0 Ghz?

Alternatively, you can use the formula $$ P(A|B) = \frac{P(A \cap B)}{P(B)}. $$ Here, the event $B$ is that the microprocessor is an Intel, and the event $A$ is that it is a $2.0$ Ghz processor. To find the probability of $A$ given $B$, you must determine the probability that a randomly chosen processor is both Intel and $2.0$ Ghz (what proportion of the processors posess both these properties?) and divide that by the probability that the processor is Intel.

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