Question

If A and B are two dependent events, Then
P(A)P(B/A)=P(B)P(A/B)
P(A/B)=P(B/A)
P(A/B)=P(A)
P(A)=P(B)​

Answer 1

Answer:

Given P(A)=1/2 and P(B)=1/5

we know that for two independent events A,B.

⇒ P(A∩B)=P(A)*P(B)

⇒P(A∩B)=1/2∗1/5=1/10

⇒1) P(A∪B)=P(A)+P(B)-P(A∩B)

=1/2+1/5−1/10

=3/5

⇒2) P(A/B)=P(A∩B)/P(B)

=

(1/5)

(1/10)

=

2

1

3)P(A/A∪B)=P(A∩(A∪B))/P(A∪B) [ since P(A∩(A∪B))=P(A)]

P(A/A∪B)=P(A)/P(A∪B)

=

(3/5)

(1/2)

=

6

5

4)P(A∩B/(A

′

∪B

′

)=

P(A

′

∪B

′

)

P((A∩B)∩(A

′

∪B

′

))

=

P(A

′

∪B

′

)

P((A∩B)∩(A∩B)

′

)

=0