Question
5) Eli Lilly and Pfizer sell competing remedies for male pattern baldness. There is a 3 out of 10 chance that Lilly's drug will be a blockbuster (blockbusters are drugs that generate revenues of at least 1 billion dollars). There is a 5 out of 10 chance that Pfizer's drug will be a blockbuster but there is only a 1 in 20 chance that both will be blockbusters. a) What is the probability that at least one of the drugs turns out to be a blockbuster? b) What is the probability that Lilly's drug is a blockbuster given that Pfizer's drug is a blockbuster? e) What is the probability that Lilly's drug is not a blockbuster given that Pfizer's drug is a blockbuster?
Explanation / Answer
E = Eli 's drug succeeds
P = Pfizer's drug succeeds
P (E) = 0.3
P(P) = 0.5
P ( E and P ) 0.05
So,
P (E or P) = 1 - P(nobody becomes a block buster)
= 1 - (0.5 * 0.7)
= 1 - 0.35
= 0.65
b)
P(E | P) = P ( E and P) / P(P)
= 0.05 / 0.5
= 0.1
c)
P(E' | P) = (0.7)*(0.5) / [0.7*0.5]+ 0.05
=0.875
Hope this helps.