The Food and Drug Administration has veto power over the choice of drug names. In 2004, it used this power regularly, rejecting 36% of the names proposed by companies for reasons such as sounding too...

The Food and Drug Administration has veto power over the choice of drug names. In 2004, it used this power regularly, rejecting 36% of the names proposed by companies for reasons such as sounding too much like another product (and causing confusion at the pharmacy). Suppose that a company spends
500,000 developing each proposed name, but there’s a 50-50 chance of a name being rejected.⁶

(a) If the review of names occurs independently, what is the probability that the company will spend more than
1 million developing a name?

(b) What is the expected cost of developing a name? [Hint: For any value
 and