4. Probability

Soccer? In a survey of 500 randomly selected Americans, it was determined that 22 play soccer. What is the probability that a randomly selected American plays soccer?

Matching Probabilities In Exercises 11-16, match the event with its probability.

a. 0.95

b. 0.005

c. 0.25

d. 0

e. 0.375

f. 0.5

14. A game show contestant must randomly select a door. One door doubles her money while the other three doors leave her with no winnings. What is the probability she selects the

door that doubles her money?

"Randomly Playing Songs

Suppose a Spotify playlist you just created has 13 tracks. After listening to the playlist, you decide that you like 5 of the songs. The random feature on Spotify is set up to play each of the 13 songs once in a random order. Find the probability that among the first 4 songs played:

b. You like 3 of them;

"

Roulette

In the game of roulette, the wheel has 38 slots numbered 0, 00, 1, 2, …, 36. A metal ball is spun around the wheel and can land in any of the slots. The slots numbered 0 and 00 are green, the odd numbers are red, and the even numbers are black..

d. Determine the probability that the metal ball lands in both the number 31 slot and a black slot at the same time. What term is used to describe this event?

Classifying Types of Probability In Exercises 53-58, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.

55. An analyst feels that the probability of a team winning an upcoming game is 60%.

What method of assigning probabilities to a simple event uses relative frequencies?

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

Square Peg Sydney Smith wrote in “On the Conduct of the Understanding” that it is impossible to fit a square peg in a round hole.

In Exercises 6–10, use the following results from tests of an experiment to test the effectiveness of an experimental vaccine for children (based on data from USA Today). Express all probabilities in decimal form.

If 1 of the 1602 subjects is randomly selected, find the probability of getting 1 that developed flu.

2. Determine whether each number could represent the probability of an event. Explain your reasoning. b. 333.3%

In Exercises 9–12, assume that 100 births are randomly selected. Use subjective judgment to describe the given number of girls as (a) significantly low, (b) significantly high, or (c) neither significantly low nor significantly high.

75 girls.

Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.

Touch Therapy When she was 9 years of age, Emily Rosa did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily’s hand without seeing it and without touching it. Among 280 trials, the touch therapists were correct 123 times (based on data in “A Close Look at Therapeutic Touch,” Journal of the American Medical Association, Vol. 279, No. 13).

a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses?

You are planning a trip to a water park tomorrow and the weather forecaster says there is a 70% chance of rain. Explain what this result means.

In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2, ..., 36. (See the photo.) To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots.

b. Determine the probability that the metal ball falls into the slot marked eight. Interpret this probability.

Finding Odds in Roulette A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number.

a. What is your probability of winning?

Made in America In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, “When you see an ad emphasizing that a product is ‘Made in America,’ are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?” The results of the survey, by age group, are presented in the contingency table below.

f. Write a few sentences describing any observed relationship between the likelihood to buy and age.