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The event the number 9 car wins the race is A and the event the number 8 car wins the race is...

Question:

The event the number 9 car wins the race is A and the event the number 8 car wins the race is B. If these events are mutually exclusive events, using {eq}P (A) = 0.39 {/eq}, and {eq}P (B) = 0.31 {/eq}, what is {eq}P(A|B) {/eq}?

Mutually exclusive events

When the two events {eq}A {/eq} and {eq}B {/eq} are mutually exclusive, then {eq}P (A and B) {/eq} equal zero because two events cannot occur together or at same time.

When event {eq}A {/eq} happens, it excludes event {eq}B {/eq}.

Answer and Explanation:

It is given that {eq}P (A) {/eq} = 0.39 and {eq}P (B) {/eq} = 0.31

Since the events are mutually exclusive, {eq}P (A and B) {/eq} = 0

Now,

{eq}P (A|B) = \frac{P (A and B)}{P (B)} {/eq}

{eq}P (A|B) = \frac{0}{P (B)} {/eq}

Therefore, {eq}P (A|B) {/eq} = 0


Learn more about this topic:

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Mutually Exclusive in Statistics: Definition, Formula & Examples

from High School Algebra II: Help and Review

Chapter 25 / Lesson 8
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