A box contains 15 chips where 5 are defective. If the random samples of 3 chips are drawn, what is the probability that exactly two are defective?
Answers
Step-by-step explanation:
Out of 15 balls 5 are defective. Probability of selecting a defective balls =
15
5
=
3
1
Now we are selecting a 5 balls at random
i.e;
15
C
5
1 none of them is defective:-
Now we must select from 10 good balls i.e;
10
C
5
P(A)=
15
C
5
10
C
5
=
(15−5)!5!
15!
(10−5)!5!
10!
=
5!5!
10!
×
15!
10!×5!
=
5!
5!×6×7×8×9×10
×
10!×11×12×13×14×15
10!
P(A)=
11×13
3×4
=
143
12
2 only one is defective:-
So we should have 4 good and 1 defective
i.e;
15
C
5
(
10
C
4
)(
5
C
1
)
=
(15−5)!5!
15!
(10−4)!4!
10!
(5−1)!1!
5!
=
6!4!4!
10!5!
×
15!
10!5!
=
5!×6!4!4!
10!5!
×
10!×15×14×13×12×11
10!5!×5
=
6×11×12×13×14×15
5×6×7×8×9×10×5
=
143
50
3 Atleast one is defective:-
Probability atleast one of them is defective
=P(A)⇒1−P(A)
1−
143
12
=
143
143−12
=
143
131