What is the probability that exactly 1 of her next 3 patients are allergic to we

Question

What is the probability that exactly 1 of her next 3 patients are allergic to weeds? In order to receive full credit, you must show all work in an organized manner in addition to providing the correct answer.

What is the probability that none of her next 3 patients are allergic to weeds? Enter your final answer as a decimal rounded to four decimal places.

Use the Following Text for Questions 36-37:

Suppose that the four inspectors at a film factory are supposed to stamp the expiration date on each package of film at the end of the assembly line.

John is responsible for stamping 25% of the packages, but forgets 1 of every 200

Tom is responsible for 45%, but forgets 1 of every 100

Jeff is responsible for 20%, but forgets 1 of every 80

Pat is responsible for 10%, but forgets 1 of every 200

Source: Walpole, R.E., Myers, R.H., Myers, S.L., & Ye, K. (2012). Probability & Statistics for Engineers & Scientists. Boston, MA: Pearson.

What is the probability that a customer will obtain a package of film that does not show the expiration date? In order to receive full credit, you must show all work in an organized manner in addition to providing the correct answer. Please do not round any values throughout your computations nor when reporting your final answer.

If a customer complains that her package of film does not show the expiration date, what is the probability that it was inspected by John? In order to receive full credit, you must show all work in an organized manner in addition to providing the correct answer.  Please do not round any values throughout your computations nor when reporting your final answer.

Explanation / Answer

1. The probability that a customer obtains a package of film that does not show the expiration date is when the package is made by John and he he forgets the stamp or the package is made by Tom and he forgets the stamp and so on

Hence required probability = P(John packs).P(John forgets) + P(Tom packs).P(Tom forgets) + ..

=0.25*1/200 + 0.45*1/100 + 0.2*1/80 + 0.1*1/200 = 0.00875

2. Let event A= package does not show expiration date

B = Packed by John

P(B|A) = P(A|B).P(B)/P(A) = 1/200*0.25/0.00875 = 1/7

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