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 indep…

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asked Jul 9, 2020 6.4k views

2 Answers

Giovanni Le Grand · Answer 1 · 2020-07-13T02:53:38+0000

Answer:

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.