Problem

The Motor Vehicle Department has found that the probability of a person passing the test for a driver's license on the first try is 0.72 . The probability that an individual who fails on the first test will pass on the second try is 0.81 . Find the probability that an individual fails both the first and second tests. $\mathrm{P}$ (fails both the first and second tests) $=$ (Simplify your answer. Type an integer or a decimal. Round to the nearest hundredth.)

Solution

Step 1 :The probability of an event not happening is 1 minus the probability of the event happening. So, the probability of failing the first test is \(1 - 0.72 = 0.28\).

Step 2 :The probability of failing the second test, given that the first test was failed, is \(1 - 0.81 = 0.19\).

Step 3 :The probability of both events happening is the product of their probabilities. So, the probability of failing both tests is \(0.28 * 0.19\).

Step 4 :Final Answer: The probability that an individual fails both the first and second tests is approximately \(\boxed{0.0532}\).

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Source: https://solvelyapp.com/problems/8vzn8DRxW4/

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