A local business, Stats For You, is trying to update their security and has decided to replace their traditional keypads at each entrance with a key card entry system. Employees would use their key...

A local business, Stats For You, is trying to update their security and has decided to replace their traditional keypads at each entrance with a key card entry system. Employees would use their key card IDs to swipe in and out each day rather than entering a common PIN (personal identification number) that can be easily stolen upon view.  Each employee will need to have their key card encoded properly to open the doors otherwise they will need to return to the Central Office to have it encoded again.

Based on previous companies transitioning to this model, Stats For You estimates the overall key card failure rate, the percent of key cards that will need to be encoded again, to be 15 percent. It can be assumed that the key card failures are independent.

a) What is the probability that in the first 50 key cards that are encoded, more than 7 people need to return to the Central Office to have their card encoded again?

b) On average, out of the first 200 key cards that are encoded, how many will not have to be encoded again?

c) What is the probability that in the first 200 key cards that are encoded, the first card that needs to be encoded again occurs on the 10^th or 11^th card?