Question

In one​ country, there exists a food and drug administration that has veto power over the choice of drug names. Last​ year, it used this power​ regularly, rejecting 39​% of the names proposed by companies for reasons such as sounding too much like another product. Suppose that a company spends ​$700,000 developing each proposed​ name, but​ there's a​ 50-50 chance of a name being rejected. If the review of names occurs​ independently, what is the probability that the company will spend more than ​$2,100, 000 developing a​ name?

Answer 1

Since company spends ​$700,000 developing each proposed​ name so for 3 reviews company need to spend ​$700,000 * 3 = ​$2,100,000. That is company will spend more than ​$2,100, 000 developing a​ name, if more than three names rejected.

Let X is a random variable shows the number of rejected. Here X has geometric distribution with parameter p = 0.50. The probability that the company will spend more than ​$2,100, 000 developing a​ name is

Answer: 0.125