Respuesta :
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 = [tex]\frac{^{22}C_0}{^{24}C_6}[/tex]
The probability that 1 train will pass her house in a 6-hour time period = [tex]\frac{^{22}C_1}{^{24}C_6}[/tex]
The probability that 2 train will pass her house in a 6-hour time period = [tex]\frac{^{22}C_2}{^{24}C_6}[/tex]
The probability that 3 train will pass her house in a 6-hour time period = [tex]\frac{^{22}C_3}{^{24}C_6}[/tex]
So, the probability that at most 4 trains will pass her house in a 6-hour time period = [tex]\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}[/tex]
= [tex]0.01332[/tex]
Hence the probability that at most 4 trains will pass her house in a 6-hour time period is 0.01332
