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

Answer:

0.01332

Step-by-step 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 = $\frac{^{22}C_0}{^{24}C_6}$

The probability that 1 train will pass her house in a 6-hour time period = $\frac{^{22}C_1}{^{24}C_6}$

The probability that 2 train will pass her house in a 6-hour time period = $\frac{^{22}C_2}{^{24}C_6}$

The probability that 3 train will pass her house in a 6-hour time period = $\frac{^{22}C_3}{^{24}C_6}$

So, the probability that at most 4 trains will pass her house in a 6-hour time period = $\frac{^{22}C_0}{^{24}C_6}+\frac{^{22}C_1}{^{24}C_6}+\frac{^{22}C_2}{^{24}C_6}+\frac{^{22}C_3}{^{24}C_6}$

                  = $0.01332$

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