SECTION 3.3 The Addition Rule 159 TRY IT YOURSELF 2 1. A die is rolled. Find the probability of rolling a 6 or an odd number. 2. A card is selected from a standard deck of 52 playing cards. Find the probability that the card is a face card or a heart. Answer: Page A38 Finding Probabilities of Mutually Exclusive Events The frequency distribution shows volumes of sales (in dollars) and the number of months in which a sales representative reached each sales level during the past three years. Using this sales pattern, find the probability that the sales representative will sell between $75,000 and $124,999 next month. Sales volume (in dollars) Months 0–24,999 3 25,000– 49,999 5 50,000–74,999 6 75,000–99,999 7 100,000–124,999 9 125,000–149,999 2 150,000–174,999 3 175,000–199,999 1 SOLUTION To solve this problem, define events A and B as A = 5monthly sales between $75,000 and $99,9996 and B = 5monthly sales between $100,000 and $124,9996. The events are mutually exclusive, as shown in the Venn diagram. Monthly sales between $100,000 and $124,999 All other monthly sales Monthly sales between $75,000 and $99,999 Monthly Sales Volume Because events A and B are mutually exclusive, the probability that the sales representative will sell between $75,000 and $124,999 next month is P1A or B2 = P1A2 + P1B2 = 7 36 + 9 36 = 16 36 = 4 9 ≈ 0.444. TRY IT YOURSELF 3 Find the probability that the sales representative will sell between $0 and $49,999. Answer: Page A38 EXAMPLE 3 Picturing the World A survey of 10,121 adults asked them how often they have had trouble sleeping in a recent span of seven days. Overall, 37% said less than one day; 30% said one to two days; 19% said three to four days; and 14% said five to seven days, as shown in the pie chart. (Source: Pew Research) How often have you had trouble sleeping in the past seven days? Three to four days 19% Five to seven days 14% Less than one day 37% One to two days 30% A U.S. adult is selected at random. What is the probability that when asked how often the adult has had trouble sleeping in the past seven days, the response will be “less than one day” or “one to two days?”
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