Exercise 11 Page 929

We want to determine whether the events are mutually exclusive and find the probability of their union. We will do these things one at a time.

Mutually Exclusive

Events that cannot occur at the same time are mutually exclusive. Mutually exclusive events have no outcomes in common. For example, because it is not possible to toss a coin and obtain heads and tails at the same time, these two events are mutually exclusive.

The coin can only land on one side, so we cannot get both heads and tails. Therefore, A and B are mutually exclusive events.

Probability

Now, we can find the probability that the coin lands on either heads or tails.

Addition Rules for Probability
If A and B are mutually exclusive events, the probability that A or B will occur is P(AorB)=P(A)+P(B).	If A and B are not mutually exclusive events, the probability that A or B will occur is P(AorB)=P(A)+P(B)-P(AandB).

We know that the coin has 2 sides. Out of these, there is 1 side called heads and 1 called tails. Now, we can calculate P(A) and P(B). P(A)&=1/2 l← ← lHeads Total sides P(B)&=1/2 l← ← lTails Total sides Finally, considering that A and B are mutually exclusive events, let's calculate P(AorB).

P(AorB)=P(A)+P(B)

SubstituteII

P(A)= 1/2, P(B)= 1/2

P(AorB)=1/2+ 1/2

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Simplify right-hand side

AddFrac

Add fractions

P(AorB)=2/2

QuotOne

a/a=1

P(AorB)=1

WritePercent

Convert to percent

P(AorB)=100 %

We found that P(Heads or tails) is equal to 100 %.