5. [-/3.54 Points] DETAILS BBUNDERSTAT12 5.2.016.MI.S. MY NOTES ASK YOUR TEA Richard has just been given a 8-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all eight questions, find the indicated probabilities. (Round your answers to three decimal places.) In USE SALT (a) What is the probability that he will answer all questions correctly? (b) What is the probability that he will answer all questions incorrectly? (c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table Then use the fact that P(r 2 1) = 1 - P(r = 0). Compare the two results. Should they be equal? Are they equal? If not, how do you account for the difference? They should not be equal, but are equal. They should be equal, but may differ slightly due to rounding error. They should be equal, but differ substantially. They should be equal, but may not be due to table error. (d) What is the probability that Richard will answer at least half the questions correctly? 6. [-/3.54 Points] DETAILS BBUNDERSTAT12 5.2.017.MI.S. MY NOTES ASK YOUR TEACHER Before 1918, approximately 60% of the wolves in a region were male, and 40% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 65% of wolves in the region are male, and 35% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.) In USE SALT (a) Before 1918, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male? What is the probability that 9 or more were female? What is the probability that fewer than 6 were female? (b) For the period from 1918 to the present, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male? What is the probability that 9 or more were female? What is the probability that fewer than 6 were female