The probability that exactly 1 train will pass Mary's house is 0.00889.
According to the given question.
On average, 18 trains pass by Mary's house daily i.e. in 24 hours.
As, we know that "Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event".
Therefore,
The probability that exactly one train will pass Mary's house in a 3 hour period
= [tex]\frac{^{18C_{1} } }{^{24} C_{3} }[/tex]
[tex]= \frac{\frac{18!}{1!\times17!} }{\frac{24!}{3!\times 21!} }[/tex]
[tex]= \frac{18}{\frac{24\times23\times22}{3\times2\times1} }[/tex]
[tex]=\frac{18}{8\times23\times\ 11}[/tex]
= 18/2024
= 0.00889
Hence, the probability that exactly 1 train will pass Mary's house is 0.00889.
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