Exercise 3 Page 929

Events are mutually exclusive when they cannot occur at the same time. Conversely, they are considered overlapping when they have outcomes in common. The following rules apply for the probability of these types of compound events.

Mutually Exclusive Events	Overlapping Events
P(AorB)= P(A)+P(B)	P(AorB)= P(A)+P(B)-P(AandB)

We know that there 4 gift cards, 6 coffee mugs, 7 DVDs, 10 CDs, and 3 gift baskets to choose from. Now, we can calculate the total number of rewards. 4+ 6+7+ 10+3= 30 ← Rewards Next, let A be receiving a gift card, B be receiving a coffee mug, and C be receiving a CD. Since the employee chooses their reward only once, these events are mutually exclusive. Finally, we can calculate P(A), P(B), and P(C). P(A)&=4/30 l← ← lGift cards Total rewards [1em] P(B)&=6/30 l← ← lCoffee mugs Total rewards [1em] P(C)&=10/30 l← ← lCDs Total rewards With this information we want to find the value of P(AorBorC).

P(AorBorC)=P(A)+ P(B)+P(C)

SubstituteValues

Substitute values

P(AorBorC)= 4/30+ 6/30+ 10/30

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Simplify right-hand side

AddFrac

Add fractions

P(AorBorC)=20/30

ReduceFrac

a/b=.a /10./.b /10.

P(AorBorC)=2/3

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Convert to percent

CalcQuot

Calculate quotient

P(AorBorC)=0.6

WritePercent

Convert to percent

P(AorBorC)=66.6 %

RoundInt

Round to nearest integer

P(AorBorC)≈67 %

The probability of receiving a gift card, coffee mug, or CD is equal to 23 or about 67 %.