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5:37 5:37Pick 10 Lottery For the New York Pick 10 lottery, the player first selects 10 numbers from 1 to 80. Then there is an official drawing of 20 numbers from 1 to 80. The prize of \$500,000 is won if the 10 numbers selected by the player are all included in the 20 numbers that are drawn. Find the probability of winning that prize.
Shared Birthdays Find the probability that of 25 randomly selected people, at least 2 share the same birthday.
Unseen Coins A statistics professor tosses two coins that cannot be seen by any students. One student asks this question: “Did one of the coins turn up heads?” Given that the professor’s response is “yes,” find the probability that both coins turned up heads.
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.
Composite Drug Test Based on the data in Table 4-1, assume that the probability of a randomly selected person testing positive for drug use is 0.126. If drug screening samples are collected from 5 random subjects and combined, find the probability that the combined sample will reveal a positive result. Is that probability low enough so that further testing of the individual samples is rarely necessary?
Jumble Many newspapers carry “Jumble,” a puzzle in which the reader must unscramble letters to form words. The letters MHRHTY were included in newspapers on the day this exercise was written. How many ways can those letters be arranged? Identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.
