SOLUTION: During the war one truck out of nine was destroyed due to bombardment. What was the probability that exactly three out of six trucks would arrive safely ?

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Question 1190737: During the war one truck out of nine was destroyed due to bombardment. What was the probability that exactly three out of six trucks would arrive safely ?
Answer by ikleyn(52778) About Me  (Show Source):
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During the war one truck out of nine was destroyed due to bombardment.
What was the probability that exactly three out of six trucks would arrive safely ?
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It is a typical binomial distribution problem.


The probability of the success (arrive safely) in each single trial is 1/9 = 0.111111.


The number of trials is  n= 6;  the number of successful trials is  k= 3.


The formula for the probability is


    P(n= 6; k= 3; p= 0.111111) = C%5B6%5D%5E3%2A0.111111%5E3%2A%281-0.111111%29%5E%286-3%29 = 20%2A0.111111%5E3%2A0.888889%5E3 = 0.019268316,  or  0.01927  (rounded).    ANSWER

Solved.