Exercise 13 Page 929

We want to determine whether the events are mutually exclusive and find the probability of their intersection. 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.

A sum rolled on a pair of dice cannot be both 6 and 10 at the same time. Therefore, A and B are mutually exclusive events.

Probability

Now, we can find the probability that we get a sum of 6 or a sum of 10 on a pair of dice.

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 can calculate the number of total outcomes, which is also the number of times the experiment is done, for a pair of dice knowing that each die has 6 different outcomes. 6*6= 36 ← Total outcomes Out of 36 times the experiment is done, a sum of six occurs 5 times and a sum of ten occurs 3 times. Now, we can calculate P(A) and P(B). P(A)&=5/36 l← ← lSum of6 Total outcomes [0.5em] P(B)&=3/36 l← ← lSum of10 Total outcomes Finally, considering that A and B are mutually exclusive events, let's calculate P(AorB).

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

SubstituteII

P(A)= 5/36, P(B)= 3/36

P(AorB)=5/36+ 3/36

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Simplify right-hand side

AddFrac

Add fractions

P(AorB)=8/36

ReduceFrac

a/b=.a /4./.b /4.

P(AorB)=2/9

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Convert to percent

CalcQuot

Calculate quotient

P(AorB)=0.2

RoundDec

Round to 3 decimal place(s)

P(AorB)≈0.222

WritePercent

Convert to percent

P(AorB)≈22.2 %

We found that P(Sum of 6or sum of10) is equal to 29 or about 22.2 %.