A robot is going to attempt the same task 100 times. Each time it tries, it will either succeed or fail to succeed in completing the task. Say the robot does not learn from its tries, so each attempt at the task is independent of the others. On a given attempt, the probability of the robot succeeding is 0.85.

a. What is the probability that the robot succeeds less than or equal to 80 times? Write out the theoretical form and use R to compute the numerical value.

b. Use the compliment rule to reduce the number of operations needed in part a. Find another way to compute the needed probability