5 Eli Lilly and Pfizer sell competing remedies for male patt

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?

Solution

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.