Exercise 8 Page 929

Can both events occur at the same time?

Mutually exclusive or not? Mutually exclusive.
Probability: 213 or about 15.4 %

Practice makes perfect

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.

Rules for Probability
If A and B are mutually exclusive events, the probability that A and B will occur is P(AandB)=0.	If A and B are not mutually exclusive events, the probability that A and B will occur is P(AandB)≠0.

Let A be drawing a jack and B be drawing a six from a standard deck of cards.

There is no card in the deck that is both a jack and a six. Therefore, A and B are mutually exclusive events.

Probability

Now we can find the probability that the card drawn is either a jack or a six.

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 there are 52 cards in the deck. Out of these, 4 cards are jacks and 4 cards are numbered 6. Now, we can calculate P(A) and P(B). P(A)&=4/52 l← ← lJacks Total cards P(B)&=4/52 l← ← lCards number6 Total cards Finally, considering that A and B are mutually exclusive events, let's calculate P(AorB).

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

SubstituteII

P(A)= 4/52, P(B)= 4/52

P(AorB)=4/52+ 4/52

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Simplify right-hand side

AddFrac

Add fractions

P(AorB)=8/52

ReduceFrac

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

P(AorB)=2/13