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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.

Respuesta :

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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
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ANSWER

EXPLANATION

Events A and B are independent events if and only if

[tex]P(A \: and \: B)=P(A) \times P(B)[/tex]

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

[tex]P(A) = 0.65[/tex]

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

[tex]P(B) = 0.76[/tex]

and

[tex]P(A \: and \: B)=0.494[/tex]

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

[tex]P(A \: and \: B)=0.65 \times 0.76[/tex]

[tex]P(A \: and \: B)=0.494[/tex]

Since

[tex]P(A \: and \: B)=P(A) \times P(B)[/tex]

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

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