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 massage

  These 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.