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please answer and explain 1. High school seniors with strong academic records apply to the nation's most selective colleges in greater numbers each year.Because the number of slots remains relatively stable some colleges reject more early applicants.Suppose that for a recent admissions class,an Ivy League college received 2851 applications for early admission Of this group,it admitted 1033 students early.rejected 854 outright,and deferred 964 to the regular admission pool for further consideration.In the past,this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375.Let E,R and D represent the events that a student who applies for early admission is admitted early, rejected outright,or deferred to the regular admissions pool. a.Use the data to estimate PE.P(R,and PD b.Are events E and D mutually exclusive?Find P(ED) For the 2375 students who were admitted,what is the probability that a randomly selected student was accepted during early admission 1 Suppose a student applies for early admission What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process? 2.According to a 2018 article in Esquire magazine,approximately 70% of males over age 70 will develop cancerous cells in their prostate.Prostate cancer is second only to skin cancer as the most common form of cancer for males in the United States.One of the most common tests for the detection of prostate cancer is the prostate-specific antigen (PSAtest However this test is known to have a high false-positive rate (tests that come back positive for cancer When no cancer is present.Suppose there is a 0.02 probability that a male patient has prostate cancer before testing.The probability of a false-positive test is 0.75.and the probability of a false-negative (no indication of cancer when cancer is actually present) is 0.20. What is the probability that the male patient has prostate cancer if the PSA test comes back positive? What is the probability that the male patient has prostate cancer if the PSA test comes back negative? For older males.the prior probability of having cancer increases.Suppose that the prior probability of the male patient is 0.30 rather than 0.02.What is the probability that the male patient has prostate cancer if the PSA test comes back positive?What is the probability that the male patient has prostate cancer if the PSA test comes back

          please answer and explain
1. High school seniors with strong academic records apply to the nation's most selective colleges in greater numbers each year.Because the number of slots remains relatively stable some colleges reject more early applicants.Suppose that for a recent admissions class,an Ivy League college received 2851 applications for early admission Of this group,it admitted 1033 students early.rejected 854 outright,and deferred 964 to the regular admission pool for further consideration.In the past,this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375.Let E,R and D represent the events that a student who applies for early admission is admitted early, rejected outright,or deferred to the regular admissions pool. a.Use the data to estimate PE.P(R,and PD b.Are events E and D mutually exclusive?Find P(ED) For the 2375 students who were admitted,what is the probability that a randomly selected student was accepted during early admission 1 Suppose a student applies for early admission What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process? 2.According to a 2018 article in Esquire magazine,approximately 70% of males over age 70 will develop cancerous cells in their prostate.Prostate cancer is second only to skin cancer as the most common form of cancer for males in the United States.One of the most common tests for the detection of prostate cancer is the prostate-specific antigen (PSAtest However this test is known to have a high false-positive rate (tests that come back positive for cancer When no cancer is present.Suppose there is a 0.02 probability that a male patient has prostate cancer before testing.The probability of a false-positive test is 0.75.and the probability of a false-negative (no indication of cancer when cancer is actually present) is 0.20. What is the probability that the male patient has prostate cancer if the PSA test comes back positive? What is the probability that the male patient has prostate cancer if the PSA test comes back negative? For older males.the prior probability of having cancer increases.Suppose that the prior probability of the male patient is 0.30 rather than 0.02.What is the probability that the male patient has prostate cancer if the PSA test comes back positive?What is the probability that the male patient has prostate cancer if the PSA test comes back

please answer and explain 1 high school seniors with strong academic records apply to the nations most selective colleges in greater numbers each yearbecause the number of slots remains rela 85438

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