Exercise 9 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.

If we roll two fours on a pair of dice, we get doubles and a sum of 8. Therefore, A and B are not mutually exclusive events.

Probability

Now, we can find the probability that we roll doubles or a sum of 8 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 possible outcomes for a pair of dice knowing that each die has 6 different outcomes. 6*6= 36 ← Total outcomes Out of 36 possible outcomes, there are 6 outcomes that result in doubles, 5 outcomes that result in a sum of 8, and only 1 outcome that results in both. Next, we can calculate P(A), P(B), and P(AandB). P(A)&=6/36 l← ← lDoubles Total outcomes [0.5em] P(B)&=5/36 l← ← lSum of8 Total outcomes [0.5em] P(AandB)&=1/36 l ← ← lDoubles and a sum of8 Total outcomes Finally, considering that A and B are not mutually exclusive events, let's calculate P(AorB).

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

SubstituteValues

Substitute values

P(AorB)=6/36+ 5/36- 1/36

AddSubFrac

Add and subtract fractions

P(AorB)=10/36

▼

Convert to percent

ReduceFrac

a/b=.a /2./.b /2.

P(AorB)=5/18

CalcQuot

Calculate quotient

P(AorB)=0.27

RoundDec

Round to 3 decimal place(s)

P(AorB)≈0.278

WritePercent

Convert to percent

P(AorB)≈27.8 %

We found that P(Doubles or a sum of8) is equal to 1036 or about 27.8 %.