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Chapter 5: Q 68. (page 332)
Teachers and college degrees Select an adult at random. Define events D: person has earned a college degree, and T: person’s career is teaching. Rank the following probabilities from smallest to largest. Justify your answer.
The order is
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Reading the paper In a large business hotel, 40% of guests read the Los Angeles Times. Only 25% read the Wall Street Journal. Five percent of guests read both papers. Suppose we select a hotel guest at random and record which of the two papers the person reads, if either. What’s the probability that the person reads the Los Angeles Times or the Wall Street Journal?
a. Make a Venn diagram to display the outcomes of this chance process using events L:reads the Los Angeles Times and W: reads the Wall Street Journal.
b. Find P.
Mac or PC? A recent census at a major university revealed that 60% of its students mainly used Macs. The rest mainly used PCs. At the time of the census, of the school’s students were undergraduates. The rest were graduate students. In the census, of respondents were graduate students and used a Mac as their main computer. Suppose we select a student at random from among those who were part of the census and learn that the person mainly uses a Mac. Find the probability that the person is a graduate student.
Smartphone addiction? A media report claims that of U.S. teens with smartphones feel addicted to their devices. A skeptical researcher believes that this figure is too high. She decides to test the claim by taking a random sample of U.S. teens who have smartphones. Only of the teens in the sample feel addicted to their devices. Does this result give convincing evidence that the media report’s claim is too high? To find out, we want to perform a simulation to estimate the probability of getting or fewer teens who feel addicted to their devices in a random sample of size from a very large population of teens with smartphones in which 50% feel addicted to their devices.
Let = feels addicted and = doesn’t feel addicted. Use a random number generator to produce random integers from to . Record the number of ’s in the simulated random sample. Repeat this process many, many times. Find the percent of trials on which the number of ’s was or less.
Rock smashes scissors Almost everyone has played the game rock-paper-scissors at some point. Two players face each other and, at the count of , make a fist (rock), an extended hand, palm side down (paper), or a “V” with the index and middle fingers (scissors). The winner is determined by these rules: rock smashes scissors; paper covers rock; and scissors cut paper. If both players choose the same object, then the game is a tie. Suppose that Player and Player are both equally likely to choose rock, paper, or scissors. a. Give a probability model for this chance process. b. Find the probability that Player wins the game on the first throw .
Mike’s pizza - You work at Mike’s pizza shop. You have the following information about the 9 pizzas in the oven: 3 of the 9 have thick crust and 2 of the 3 thick-crust pizzas have mushrooms. Of the remaining 6 pizzas, 4 have mushrooms.
a. Are the events “thick-crust pizza” and “pizza with mushrooms” mutually exclusive? Page Number: 356 Justify your answer.
b. Are the events “thick-crust pizza” and “pizza with mushrooms” independent? Justify your answer.
c. Suppose you randomly select 2 of the pizzas in the oven. Find the probability that both have mushrooms.
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