SECTION 3.1 Basic Concepts of Probability and Counting 145 88. Individual Stock Price An individual stock is selected at random from the portfolio represented by the box-and-whisker plot shown. Find the probability that the stock price is (a) less than $21, (b) between $21 and $50, and (c) $30 or more. 10 90 80 70 60 50 40 30 20 100 12 21 30 50 94 Stock price (in dollars) Writing In Exercises 89 and 90, write a statement that represents the complement of the probability. 89. The probability of randomly choosing a person who smokes whose mother also smoked from the population of all people who smoke 90. The probability of randomly choosing a car with more than one cause for showing its “CHECK ENGINE” light from the population of vehicles showing “CHECK ENGINE” lights Extending Concepts Odds The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read “2 to 3”). In Exercises 91–96, use this information about odds. 91. A beverage company puts game pieces under the caps of its drinks and claims that one in six game pieces wins a prize. The official rules of the contest state that the odds of winning a prize are 1 : 6. Is the claim “one in six game pieces wins a prize” correct? Explain your reasoning. 92. The probability of winning an instant prize game is 1 10. The odds of winning a different instant prize game are 1 : 10. You want the best chance of winning. Which game should you play? Explain your reasoning. 93. The odds of an event occurring are 4 : 5. Find (a) the probability that the event will occur and (b) the probability that the event will not occur. 94. A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is a spade. 95. A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is not a spade. 96. The odds of winning an event A are p : q. Show that the probability of event A is given by P1A2 = p p + q . 97. Rolling a Pair of Dice You roll a pair of six-sided dice and record the sum. (a) List all of the possible sums and determine the probability of rolling each sum. (b) Use technology to simulate rolling a pair of dice and record the sum 100 times. Make a tally of the 100 sums and use these results to list the probability of rolling each sum. (c) Compare the probabilities in part (a) with the probabilities in part (b). Explain any similarities or differences.
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