Question

The probability of getting disease X (event A) is 0.65 and the probability of getting disease Y (event B) is 0.76. The probability of getting both disease X and disease Y is 0.494. Are events A and B dependent or independent?

In this scenario, A and B are ______ events.

Answer 1

The 2 events are independent since the occurrence of one doesn't affect the occurrence of the other and P(A∩B) = P(A) x P(B) = 0.65 x 0.76 = 0.494

Answer 2

ANSWER

Step-by-step explanation

Events A and B are independent events if and only if


`P(A \: and \: B)=P(A) * P(B)`

We were given that, the probability of getting disease X, which is event A is,


`P(A) = 0.65`

and the probability of getting disease Y, which is event B, is


`P(B) = 0.76`

and


`P(A \: and \: B)=0.494`

Now, let us find the probability of getting both disease X and Y,


`P(A \: and \: B)=0.65 * 0.76`


`P(A \: and \: B)=0.494`

Since


`P(A \: and \: B)=P(A) * P(B)`

The two events are independent. Therefore A and B are independent events.