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- When a fair eight-sided die (octahedron) is rolled. The outcomes of rolling this die will be the number 1 thru 8 pointing up. For example, the 8 side is pointing up in the picture. (a) Write the sample space of this experiment. (b) Compute the probability of rolling a 3. (c) Compute the probability of rolling a number is more than 5. (d) Compute the probability of rolling an odd number.Kiyo is creating a table using mosaic tiles chosen and placed randomly. She is picking tiles without looking. How does P(yellow second | blue first) compare to P(yellow second | yellow first) if the tiles are selected without replacement? If the tiles are selected and returned to the pile because Kiyo wants a different color?In the rolling of two fair dice calculate the following (refer to image).
- d) Ana tosses a 50p coin twice. What’s the probability she’ll get two heads?Diana Baniak, searching for an Ecology class, knows that it must be in one of EIGHT classrooms. Since the professor does not allow people to enter after the class has begun, and there is very little time left, she decides to try just FOUR of the rooms at random. How many of the possible different selections of FOUR rooms will succeed in locating the class? There are _______ successful selections.This exercise involves combinations. In a raffle with 11 entries, in how many ways can five winners be selected? ways
- Is the lottery fair? Power ball is a multistate lottery in which players try to guess the numbers that will turn up in a drawing of numbered balls. One of the balls drawn is the "Powerball." Matching the number drawn on the Powerball increases one's winnings. In a 17 month period, the Power ball was drawn from a collection of 35 balls numbered 1 through 35. A total of 141 drawings were made. For the purpose of this exercise, we grouped the numbers in to five categories: 1–7, 8–14, and so on. If the lottery is fair, then the winning number is equally likely to occur in any category. Following are the observed frequencies. Test the hypothesis that each of the categories is equally likely. Use the 0.05 level of significance and the P-value method with the TI-84 Plus calculator. Category 1–7 8–14 15– 21 22–28 29–35 Observed 22 20 29 32 38 Send data to Excel ) State the null and alternate hypotheses. H0: p1=p2=p3=p4=p5=?…Can you check if this amount is correctt, please:)Random outcomes For each of the following scenarios,decide if the outcome is random.a) Flip a coin to decide who takes out the trash. Is whotakes out the trash random?b) A friend asks you to quickly name a professionalsports team. Is the sports team named random?c) Names are selected out of a hat to decide roommatesin a dormitory. Is your roommate for the year random?
- Is the lottery fair? Power ball is a multistate lottery in which players try to guess the numbers that will turn up in a drawing of numbered balls. One of the balls drawn is the "Powerball." Matching the number drawn on the Powerball increases one's winnings. In a 17 month period, the Power ball was drawn from a collection of 35 balls numbered 1 through 35. A total of 143 drawings were made. For the purpose of this exercise, we grouped the numbers in to five categories: 1-7, 8-14, and so on. If the lottery is fair, then the winning number is equally likely to occur in any category. Following are the observed frequencies. Test the hypothesis that each of the categories is equally likely. Use the 0.10 level of significance and the P-value method with the TI-84 Plus calculator. Category 1-7 8-14 15-21 22-28 29-35 Observed 21 40 24 23 35 State the null hypothesis Compute the P-value Determine whether to reject H0 state the conclusionIn the BS Lottery players choose 6 numbers out of 30. They win if they choose the same 6 numbers as our machine, which selects the numbers randomly. (A) How many permutations are possible? (B) How many combinations are possible?
