A ship is fitted with three engines A, B and C. These three engines function independently of each other
with probabilities /2 , 74, 74 respectively. For ship to be operational at least two of its engines must
function. Let E denote the event that the ship is operational and E1 E2 and E3 denote the events that
engines A,B and C are functioning. Then validate the following.
(a). PE /E) = 3/16
(b) P(E/E2) = 5/16
(c) P( Exactly two engines of the ship are functioning / E) = 7/8.
Answers
P(X
1
)=
2
1
,P(X
2
)=
4
1
,P(X
3
)=
4
1
P(X)=P(X
1
∩X
2
∩X
3
c
)+P(X
1
∩X
2
c
∩X
3
)+P(X
1
c
∩X
2
∩X
3
)+P(X
1
∩X
2
∩X
3
)=
4
1
(A) P(X
1
c
/X)=
P(X)
P(X∩X
1
c
)
=
4
1
2
1
×
4
1
×
4
1
=
8
1
P(
X
exactly 2 engines
)=
4
1
(
2
1
×
4
1
×
4
1
)+(
2
1
×
4
1
×
4
3
)+(
2
1
×
4
3
×
4
1
)
=
8
7
P(
X
2
X
)=
P(X
2
)
P(X∩X
2
)
=
4
1
(
2
1
×
4
1
×
4
1
)+(
2
1
×
4
1
×
4
3
)+(
2
1
×
2
1
×
4
1
)
=
4
1
32
5
=
8
5
P(
X
1
X
)=
P(X
1
)
P(X∩X
1
=
2
1
32
7
=
16
7
Answer:
PE /E) = 3/16
(b) P(E/E2) = 5/16
(c) P( Exactly two engines of the ship are f
Step-by-step explanation:
SOLUTION
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