A coin with p{h} = p = 1 - q is tossed n times. Show that the probability that the number of heads is even equals 0.5[1 + (q - p)"].
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![A coin with p{h} = p = 1 - q is tossed n times. Show that the probability that the number
of heads is even equals 0.5[1 + (q - p)"].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71f6a4b8-527f-4030-b85a-828002701c6f%2Fe50bae04-ddf7-4eeb-a4fc-edd152d4da83%2Fr152c7u_processed.png&w=3840&q=75)
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- If a number is randomly chosen from the interval (-3,3). What is the probability that the number is less than −8/3? Suppose that a number is randomly chosen from the interval (-6,2). What is the probability that the number chosen within 2 units away from 1? NOTE: ROUND OFF your answer to FOUR DECIMAL places.What is the probability that zz is greater than −0.25express the event "taking atleast 16 credits" in terms of X and find its probability
- At a bank, there is a line of 3 people and only one cashier that serves one person at a time. The time that the cashier takes to serve each person has an exponential distribution with a mean of 5 minutes. Calculate the probability that the total time of serving the 3 people is less than 15 minutes. Assume that the serving times are independent.A professor of management has heard that eleven students in his class of 37 have landed an internship for the summer. Suppose he runs into two of his students in the corridor. a. Find the probability that neither of these students has landed an internship. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) b. Find the probability that both of these students have landed an internship.Kelly realized that 4% of his students' exams have academic integrity issues. He plans to go through the exams at random to find one with academic integrity issues. Let X be the number of exams Kelly selects until he finds one with academic integrity issues. a) Find the probability that the 18 th exam Kelly selects will be the first with academic integrity issues. State your answer as a percentage rounded your answer to 2 decimal places. b) What is the probability of finding an exam with academic integrity issues within the first 5 exams? Round your answer to 3 decimal places.
- Ezra buys a bag of cookies that contains 9 chocolate chip cookies, 7 peanut butter cookies, 4 sugar cookies and 4 oatmeal cookies.What is the probability that Ezra reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects a chocolate chip cookie? Give your answer as a fraction, or accurate to at least 4 decimal places.The table summarizes results from 980 pedestrian deaths that were caused by automobile accidents. Driver Intoxicated? Pedestrian Intoxicated? Yes No Yes 60 69 No 238 613 If one of the pedestrian deaths is randomly selected, find the probability that both the pedestrian and the driver were intoxicated. Please enter a decimal to 4 places.The number of work accidents that occur per week in a mine follows Poisson's law so that the probability of 2 accidents occurring is equal to 3/2 of the probability of an accident occurring. Calculate the probability that the time for the first accident to occur is one week.
- The probability that a new computer functions for over 10,000 hours is 0.8, the probability that it functions for over 20,000 hours is 0.4 and the probability that it functions for over 30,000 hours is 0.1. If a new computer is still working after 10,000 hours, what is the probability that i. its total life will exceed 20,000 hours;ii. its additional life will exceed 20,000 hours?Let ? be the amount of time (in minutes) a postal clerk spends with his or hercustomer. The time is known to have an exponential distribution with the average amount of timeequal to four minutes.i) Find the probability that a clerk spends four to five minutes with a randomly selected customer.ii) Find the probability that a clerk spends at least five minutes with a randomly selected customer.P(z > -2.74)Express the probability as a decimal rounded to 4 decimal places.
