The event of you going to work is a and the event of you taking leave is b. if these events are mutually exclusive events, using p(a)=0.55, and p(b)=0.10, what is p(a|b)?

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The events are mutually exclusive events, so P(A|B) is 0.

In this question,

If two events are mutually exclusive, there is no chance that both events will occur. Being the intersection an operation whose result is made up of the non-repeated and common events of two or more sets, that is, given two events A and B, their intersection is made up of the elementary events that they have in common, then

⇒ A ∩ B = 0

Now the conditional probability, P(A|B) = [tex]\frac{P(A \cap B )}{P(B)}[/tex]

⇒ [tex]\frac{0}{0.10}[/tex]

⇒ 0.

Hence we can conclude that the events are mutually exclusive events, so P(A|B) is 0.

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