Exercise 35 Page 931

Let's look at the given table with the type and number of prizes.

We want to find the probability that the first customer wins manicure or a massage. We can define the following events.

• A — the customer wins a manicure
• B — the customer wins a massageThese two events cannot happen at the same time, therefore they are mutually exclusive events. Let's recall the formula for finding it.

  Probability of Mutually Exclusive Events

  If two events A and B are mutually exclusive, then the probability that A or B occurs is the sum of the probabilities of each individual event. P(A orB) = P(A) + P(B)

  In order to find P(A) and P(B), we will use theoretical probability. P = Favorable Outcomes/Possible Outcomes The number of possible outcomes will be the sum of numbers of all possible prizes a customer can win. 10+6+3+1 = 20 There are 10 manicures to win, so the number of favorable outcomes for the event A is equal to 10. While for the event B, the number of favorable outcomes is 3. We are ready to calculate P(A) and P(B). P(A) &= 10/20 [0.5em] P(B) &= 3/20 We are ready to use the formula for P(A or B) and find the probability that the first customer wins a manicure or a massage.

  P(A orB) = P(A) + P(B)

  SubstituteII

  P(A)= 10/20, P(B)= 3/20

  P(A orB) = 10/20 + 3/20

  AddFrac

  Add fractions

  P(A orB) = 13/20

  UseCalc

  Use a calculator

  P(A orB) = 0.65

  This corresponds to answer D.