Exercise 25 Page 936

Events are mutually exclusive when they cannot occur at the same time. Or, 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 are 52 cards in the standard deck of cards and that there are 13 cards in each suit. Now, let A be drawing a 10 and B be drawing a diamond.

Out of 52 cards, there are 4 cards number ten, 13 diamond cards and 1 diamond ten card. Since there is a card that is both a 10 and a diamond, these events are not mutually exclusive. Finally, we can calculate P(A), P(B), and P(AandB). P(A)&=4/52 l← ← lCards number10 Total cards P(B)&=13/52 l← ← lDiamonds Total cards P(AandB)&=1/52 l← ← lDiamond 10s Total cards With this information we want to find the value of P(AorB).

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

SubstituteValues

Substitute values

P(AorB)=4/52+ 13/52- 1/52

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Simplify right-hand side

AddSubFrac

Add and subtract fractions

P(AorB)=16/52

ReduceFrac

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

P(AorB)=4/13

The probability of drawing a 10 or a diamond card is equal to 413.