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 0.0496. 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 the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    3      
p = the probability of a success =    0.0496      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.858458456

Thus, P(at least one) = 1 - P(0) =   0.141541544 [ANSWER]

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Is there any reason why the probability might be wrong?

Yes, because as these are cars by a family, they might not be independent, which is the assumption of binomial distribution.