Respuesta :
Answer:
The probability that fewer than 2 troubles will be repaired on the same day is:
0.015576
Step-by-step explanation:
We have to use the Binomial function is n=order to calculate the probability of r successes out of the n-events.
We know that the probability of r success out of the n-events is given by:
[tex]P(X=r\ successes)=n_C_r\cdot p^r\cdot (1-p)^{n-r}[/tex]
where p is the probability of an success.
Here we have:
n=5 and r=0,1.
since we are asked to find the probability that fewer than 2 troubles will be repaired on the same day.
i.e we have to find:
[tex]P(X<2)=P(X=0)+P(X=1)[/tex]
Also p=0.75 ( since, likelihood is 0.75 that troubles in a residential service can be repaired on the same day )
Hence,
[tex]P(X=0)=5_C_0\cdot (0.75)^{0}\cdot (1-0.75)^{5-0}\\\\P(X=0)=1\cdot 1\cdot (0.25)^5\\\\P(X=0)=0.000976[/tex]
and
[tex]P(X=1)=5_C_1\cdot (0.75)^{1}\cdot (0.25)^{5-1}\\\\P(X=1)=5\cdot (0.75)\cdot (0.25)^4\\\\P(X=1)=0.0146[/tex]
Hence,
[tex]P(X<2)=0.000976+0.0146\\\\P(X<2)=0.015576[/tex]
Hence, the probability that fewer than 2 troubles will be repaired on the same day is:
0.015576
