Question

The probability of event A is 0.65, and the probability of event B is 0.76. The probability of both event A and event B occurring is 0.494. Are events A and B dependent or independent?

Answer 1

Answer:independent

Explanation:

Answer 2

Event A and B are independent

Explanation:

Events A and B are independent if and only if

`P(A \cap B) = P(A) \cdot P(B)`

As per the statement:

The probability of event A is 0.65 and the probability of event B is 0.76.

⇒
`P(A) = 0.65` and
`P(B) = 0.76`

It is also given that the probability of both event A and event B occurring is 0.494.

`P(A \cap B) =0.494`

Find:
`P(A \cap B)`

`P(A) \cdot P(B) = 0.65 \cdot 0.76`

Simplify:

`P(A \cap B) = 0.494`

⇒
`P(A) \cdot P(B) =P(A \cap B)`

therefore, Events A and B are independent.