The probability of a randomly selected car crashing during a

The probability of a randomly selected car crashing during a year in a certain country is 0.0465. If a family has three cars, find the probability that at least one of them has a car crash during a year. Is there any reason why the probability might be wrong? The probability that at least one of them has a crash during the year is (Round to four decimal places as needed.)

Solution

Note that

P(at least one car crashes) = 1 - P(no car crashes)

As

P(car does not crash) = 1 - P(car crashes)

P(car does not crash) = 1 - 0.0465

P(car does not crash) = 0.9535

Thus,

P(no car crashes) = (0.9525)^3 = 0.866886

as there are 3 cars. Thus,

P(at least one car crashes) = 1 - P(no car crashes)

P(at least one car crashes) = 1 - 0.866886

= 0.1331 [ANSWER]

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This probability could be wrong as the family may have been using just one car most of the time, not all the cars, or the attitude of the driver of each car are difference, etc.