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At the height of the Covie-19 pandemic, Mark Lampert and his coauthors compared the search for a therapeutic agent to the need to take lots of shots on the goal in low scoring games like soccer and hockey. Although each shot hak low probability, when you take many, the laws of probability predict eventual success. They note that there are about 100 drugs now being tested. "With so many shots on goal. if each of these candidates has even a 5 percent chance of success, the probability that at least one impactful drug emerges is over 99 percent." [R306] (a) Why do the authors believe that the probability that all the drugs falls is (1 - 0.05) 100, (b) Evaluate that expression and confirm that there is more tha

At the height of the Covie-19 pandemic, Mark Lampert and his coauthors compared the search for a therapeutic agent to the need to take lots of shots on the goal in low scoring games like soccer and hockey. Although each shot hak low probability, when you take many, the laws of probability predict eventual success. They note that there are about 100 drugs now being tested. "With so many shots on goal. if each of these candidates has even a 5 percent chance of success, the probability that at least one impactful drug emerges is over 99 percent." [R306] (a) Why do the authors believe that the probability that all the drugs falls is (1 - 0.05) 100, (b) Evaluate that expression and confirm that there is more tha

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 39E: The following problem submitted by Daniel Hahn of Blairstown, Iowa, appeared in the Ask Marilyn...
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4 At the height of the Covie-19 pandemic, Mark Lampert and his coauthors compared the search for a therapeutic agent to the need to take lots of shots on the goal in low scoring games like soccer and hockey. Although each shot hak low probability, when you take many, the laws of probability predict eventual success. They note that there are about 100 drugs now being tested. "With so many shots on goal. if each of these candidates has even a 5 percent chance of success, the probability that at least one impactful drug emerges is over 99 percent." [R306] (a) Why do the authors believe that the probability that all the drugs falls is (1 - 0.05) 100, (b) Evaluate that expression and confirm that there is more than a 99 percent chance that at feast one drug succeeds. (c) The implicit assumption in the first question is that the individual probabilities of success are independent. Suppose that the 100 drugs represent just five different kinds of drugs and that each kind has a 5 percent chance of success. Calculate the probability that at least one kind succeeds.
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