Question

On average, Bethany has noticed that 22 trains pass by her house daily (24 hours) on the nearby train tracks. What is the probability that at most 4 trains will pass her house in a 6-hour time period

Answer 1

0.01332

Explanation:

Given : On average, Bethany has noticed that 22 trains pass by her house daily (24 hours) on the nearby train tracks.

To Find :What is the probability that at most 4 trains will pass her house in a 6-hour time period

Solution:

We are suppose to find the probability that at most 4 trains will pass her house in a 6-hour time period

The probability that 0 train will pass her house in a 6-hour time period =
`(^(22)C_0)/(^(24)C_6)`

The probability that 1 train will pass her house in a 6-hour time period =
`(^(22)C_1)/(^(24)C_6)`

The probability that 2 train will pass her house in a 6-hour time period =
`(^(22)C_2)/(^(24)C_6)`

The probability that 3 train will pass her house in a 6-hour time period =
`(^(22)C_3)/(^(24)C_6)`

So, the probability that at most 4 trains will pass her house in a 6-hour time period =
`(^(22)C_0)/(^(24)C_6)+(^(22)C_1)/(^(24)C_6)+(^(22)C_2)/(^(24)C_6)+(^(22)C_3)/(^(24)C_6)`

=
`0.01332`

Hence the probability that at most 4 trains will pass her house in a 6-hour time period is 0.01332