The probability is 1 in 4,014,000 that a single auto trip in the United States w

Question

The probability is 1 in 4,014,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips.

What is the probability of a fatal accident over a lifetime? (Hint: Assume independence.) (Round your answer to 4 decimal places.)

The probability is 1 in 4,014,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips.

What is the probability of a fatal accident over a lifetime? (Hint: Assume independence.) (Round your answer to 4 decimal places.)

Explanation / Answer

Here,

P(accident) = 1/4014000 = 0.000000249128

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 =    50000      
p = the probability of a success = 0.000000249128      
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.012302206 = 0.0123 [ANSWER]

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