You have been 1. P(R) = 3/8 given 39 two events Rand S such that 2. P(RIS)= 3/5 3. P(STR) = 217 What is P(S) in the given context?
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Answer:
Step-by-step explanation:
P(A∪B)=P(A)+P(B)−P(A∩B)
⇒
8
5
=
8
3
+
2
1
−P(A∩B)
⇒P(A∩B)=
8
2
=
4
1
Now,
P(A
c
/B)=
P(B)
P(A
c
∩B)
=
P(B)
P(B)−P(A∩B)
=
2
1
2
1
−
4
1
=
4
2
=
2
1
=P(B)
P(A/B
c
)=
P(B
c
)
P(A∩B
c
)
=
1−P(B)
P(A)−P(A∩B)
=
1−
2
1
8
3
−
4
1
=
4
1
=P(A∩B)
Hence,
P(A
c
/B)=2P(A/B
c
)
P(A
c
/B
c
)=
P(B
c
)
P(A
c
∩B
c
)
=
1−P(B)
1−P(A∪B)
=
2
1
1−
8
5
=
4
3
and
P(B/A
c
)=
P(A
c
)
P(A
c
∩B)
=
1−P(A)
P(B)−P(A∩B)
=
1−
8
3
2
1
−
4
1
=
5
2
Thus we see that
P(B/A
c
)
P(A
c
/B
c
)
=
5
2
4
3
=
8
15
⇒8P(A
c
/B
c
)=15P(B/A
c
)
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