Question

A and B are two events. Let P(A)=0.5 , P(B)=0.9 and P(A and B)=0.15 .

Which statement is true?



A and B are independent events because P(A|B)=P(B) and P(B|A)=P(A) .

A and B are not independent events because P(A|B)=P(A) and P(B|A)=P(B) .

A and B are not independent events because P(A|B)≠P(A) .

A and B are not independent events because P(A|B)=P(B) and P(B|A)=P(A) .

Answer 1

A and B are not independent events because P(A|B)≠P(A) .

Step-by-step : test

Answer 2

option-C

Explanation:

we are given

Let P(A)=0.5

P(B)=0.9

P(A and B)=0.15

we know that

`P(A|B)=(P(Aand B))/(P(B))`

now, we can plug values

`P(A|B)=(0.15)/(0.9)`

`P(A|B)=0.16666`

but we have

P(A)=0.5

we can see that both are not equal

`P(A|B)\\eq P(A)`

so, A and B are not independent

so, option-C........Answer