HHS Tiger Math



Homework Quiz: Simulation, Probability, and Probability Rules Name__________________________1. Researchers recruited 20 volunteers- 8 men and 12 women- to take part in an experiment. They randomly assigned the subjects into two groups of 10 people each. To their surprise, 6 of the 8 men were randomly assigned to the same treatment. Should they be surprised? Design and carry out a simulation to estimate the probability that the random assignment puts 6 or more men in the same group. Follow the four step process, you may use only 1 repetitions and base your conclusion off the one repetition for time’s sake. 2. Multiple Choice: You read in a book about bridge that the probability that each of the four players is dealt exactly one aces is about 0.11. This means that: a. in every 100 bridge deals, each player has one ace exactly 11 timesb. in one million bridge deals, the number of deals on which each player has one ace will be exactly 110,000c. in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to 11%d. in a very large number of bridge deals, the average number of aces in a hand will be very close to 0.11e. none of these. 3. Stop Light: On her drive to work everyday, Ilana passes through an intersection with a traffic light. The light has a probability 1/3 of being green when she gets to the intersection. Explain how you would use each chance device to simulate whether the light is red or green on a given day. Six-sided dieRandom Number Generator 4. Canada has two official languages, English and French. Choose a Canadian at random and ask, “What is your mother tongue?” Here is a distribution of responses, combining many separate languages from the broad Asia/Pacific region:LanguageEnglishFrenchAsian/PacificOtherProbability0.630.220.06?What probability should replace “?” in the distribution? Why? What is the probability that a Canadian’s mother tongue is not English?What is the probability that a Canadian’s mother tongue is a language other than English or French?5. An American roulette wheel has 38 slots with numbers 1 through 36, 0, and 00, as shown in the figure. Of the numbered slots, 18 are red, 18 are black, and 2- the 0 and 00- are green. When the wheel is spun, a metal ball is dropped into the middle of the wheel. If the wheel is balanced, the ball is equally likely to settle in any of the numbered slots. Imagine spinning a fair wheel once. Define events B: ball lands in a black slot, and E ball lands in an even-numbered slot. (Treat 0 and 00 as even numbers).Make a two-way table that displays the sample space in terms of events B and E.525780014605000Find P(B) and P(E).Describe the event “B and E” in words. Then find P(B and E). Show your work.Explain why P(B or E) ≠P(B) + P(E). Then use the general addition rule to compute P(B or E). ................
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