In a particularly delicate process for manufacturing a particular type of experimental silicon chip, the probability of successfully producing a marketable chip is 70%. The company needs to produce 12 marketable chips, but only has the budget to manufacture 15 chips.

(a) What is the probability that they will be able to produce 12 marketable chips in at most 15 attempts?

(b) How many chips described in this problem need to be manufactured so that the probability of getting at least 12 marketable chips is 95%.

Make sure to clearly define the random variables and specify their probability distributions and parameters.

Use R for computations in the following questions and submit your R file as well.