UNO High School Problem of the Week Competition

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Problem 9

Suppose that a company is trying to introduce the newest camera phone.

The company has a marketing department that predicts whether or not each new product will be a success.
Based on yearly results, we know the following statistics of the company.
Of all new products introduced, 65% of them are successes.
We also know that 75% of their successful products were predicted to be a success, while only 30% of all failed products were actually predicted as being a success.

Given the above statistics, if this new camera phone is predicted to be a success, find the probability that the phone will be successful.

Solution