Plan B Here’s another attempt at developing a good strategy for the dice game in Exercise 33.

Instead of stopping after a certain number of rolls, you could decide to stop when your score reaches a certain number of points.

a) How many points would you expect a roll to add to your score?

b) In terms of your current score, how many points would you expect a roll to subtract from your score?

c) Based on your answers in parts

a) and b), at what score will another roll “break even”?

d) Describe the strategy this result suggests. 35.

Technology on campus 2005 Every five years, the Conference Board of the Mathematical Sciences surveys college math departments. In 2005, the board reported 37.

O-rings Failures of O-rings on the space shuttle are fairly rare, but often disastrous, events. If we are testing O-rings, suppose that the probability of a failure of any one O-ring is 0.01. Let X be the number of failures in the next 10 O-rings tested.

a) Clearly the Binomial model can be applied here. What other model might you use to model X?

b) What is the mean number of failures in the next 10 O-rings?

c) What is the probability that there is exactly one failure in the next 10 O-rings? Use the model from your answer to part a).

d) What is the probability that there is at least one failure in the next 10 O-rings? Use the model from your answer to part a).