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On New Year's Eve, the probability of a person having a car accident is 0.09. The probability of a person driving while intoxicated is 0.32 and probability of a person having a car accident while intoxicated is 0.15. What is the probability of a person driving while intoxicated or having a car accident?

Round to 2 decimal places

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Answer:

Explanation:

To calculate the probability of a person driving while intoxicated or having a car accident, we need to use the formula for the union of events:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are the events of driving while intoxicated and having a car accident, respectively.

Using the probabilities given in the problem, we can calculate:

P(intoxicated) = 0.32

P(accident) = 0.09

P(accident | intoxicated) = 0.15

To find P(intoxicated or accident), we first need to find P(intoxicated and accident). We can use the formula for the conditional probability as follows:

P(intoxicated and accident) = P(accident | intoxicated) x P(intoxicated)

P(intoxicated and accident) = 0.15 x 0.32 = 0.048

Now we can use the formula for the union of events:

P(intoxicated or accident) = P(intoxicated) + P(accident) - P(intoxicated and accident)

P(intoxicated or accident) = 0.32 + 0.09 - 0.048

P(intoxicated or accident) = 0.362

Therefore, the probability of a person driving while intoxicated or having a car accident is 0.362, or approximately 36.2%.

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