Two events A and B are mutually exclusive. If P(A) = 0.31 and P(B) = 0.35, then P(A or B) = ?

Question:

Two events A and B are mutually exclusive.

If P(A) = 0.31 and P(B) = 0.35, then P(A or B) = ?

Mutually Exclusive Events:

The rule of addition for probability calculation states the following:

{eq}P(A\bigcup B)=P(A)+P(B)-P(A\bigcap B) {/eq}

When events are mutually exclusive it means that both cannot occur simultaneously, therefore:

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

Finally, for mutually exclusive events, the rule of addition is reduced to:

{eq}P(A\bigcup B)=P(A)+P(B) {/eq}

Answer and Explanation:

We need to calculate {eq}P(A\bigcup B) {/eq}.

We know that {eq}P(A\bigcup B)=P(A)+P(B)-P(A\bigcap B) {/eq}

Since the events are mutually exclusive:

{eq}P(A\bigcap B)=0 {/eq}, therefore: {eq}P(A\bigcup B)=P(A)+P(B) {/eq}

Replacing values:

{eq}P(A\bigcup B)=0.31+0.35\\ P(A\bigcup B)=0.66\\ {/eq}


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Mutually Exclusive Events & Non-Mutually Exclusive Events

from 6th-8th Grade Math: Practice & Review

Chapter 48 / Lesson 5
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