Stat hw 1

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Feb 20, 2024

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Jackson Carney Stat 412 5/16/2022 Stat 412 HW# 1 1. The following table displays the 100 senators of the 112th U.S. Congress on January 5, 2011, viewed by political party affiliation and gender a. 17/100 b. 42/100 c. 14/25 2. The game of craps is played with two dice. A player throws both dice, winning unconditionally if he produces a natural (the sum of the numbers showing on the two dice is 7 or 11), and losing unconditionally if he throws craps (the sum is 2,3, or 12). Consider the following events: a. 4/36 b. 8/36 c. 9/36 i. C and B are mutually exclusive since C and B cannot happen at the same time ii. None of the combinations equal each other. This means that all events are independent of one another 3. In a certain county, 45% of the registered voters are Democrats, 35% are Republicans, and 20% are Independents. Sixty percent of the Democrats, 80% of the Republicans, and 30% of the Independents favored increased spending to combat terrorism. If a person chosen at random from the county does not favor increased spending to combat terrorism, what is the probability that the person is a Democrat? 18/39 4. An experiment consists of flipping a fair coin once and rolling a fair die once. What is the probability of observing a head or a six? 7/12 5. Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30% are shipped to people other than the person placing the order. Gift wrapping is requested for 60% of the orders being shipped to other people, but for only 10% of orders shipped to the person making the order a. What is the probability that a randomly selected order will be gift wrapped and sent to another person? 18% b. What is the probability that a randomly selected order will be gift wrapped? 78% c. Is gift wrapping independent of the destination of the gift? Justify your response statistically.
P(A|B) = P(A), in this case P(A|B) does not equal P(A) so these are not independent of one another 6. A spinner has equal regions numbered 1 through 15. What is the probability that the spinner will stop on an even number or a multiple of 3? 10/15 7. A survey of the male students at a junior college reveals that, 21% play soccer regularly, 22% are Latino, and half of the Latino students play soccer regularly. If a male student is selected at random, what is the probability that he is not Latino and does not play soccer regularly? 97.69% P(non-Latino and does not play soccer) 8. A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 5% of the time if the person does not have the virus. If a person tests positive, what is the probability that the person is infected? 7.44% 9. The probability that a married man will vote in a specific election is 0.50, the probability that a married woman will vote in the election is 0.60, and the probability that a married woman will vote in the election given her husband votes is 0.90. a. 9/20 b. ¾ c. 78% 10. For a four-question multiple-choice pop quiz, a student is totally unprepared and randomly guesses the answer to each question. If each question has five options, then the probability of selecting the correct answer for any given question is 1/5, or .2. With guessing, the response on one question is not influenced by the response on another question. Thus, whether one question is answered correctly is independent of whether or not another question is answered correctly. Find the probability the student passes, answering at least three questions correctly 2.72%
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