Answer:
The probability of one machine breaking down
P(X=1) = 0.13194
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 15
The probability of breaking down of each machine = 0.2
p = 0.2
q = 1-p = 1-0.2 = 0.8
Step(ii)
Let 'X' be the random variable in binomial distribution
[tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]
The probability of one machine breaking down
[tex]P(X=1) = 15_{C_{1} } (0.2)^{1} (0.8)^{15-1}[/tex]
On calculation , we get
P(X=1) = 15 ×(0.2)×(0.8)¹⁴
P(X=1) = 0.13194
Final answer:-
The probability of one machine breaking down
P(X=1) = 0.13194
