Answer:
The probability of getting 2 defective items
P(X=2) = 0.0317416
Step-by-step explanation:
Step(i):-
Given that size of the components n = 10
Given that the probability of getting the defective item
p = 3% = 0.03
q = 1-p =1- 0.03 = 0.97
Let 'X' be a random variable in a binomial distribution
[tex]P(X=r) =n_{C_{r} } p^{r} q^{n-r}[/tex]
Step(ii):-
The probability of getting 2 defective items
[tex]P(X=2) =10_{C_{2} } (0.03)^{2} (0.97)^{10-2}[/tex]
[tex]10_{c_{2} } = \frac{10!}{(10-2)!2!} = \frac{10 X 9 X8!}{8!2!} = 45[/tex]
P(X =2) = 45 × 0.000705
P(X=2) = 0.0317416
