Explain why 1/8 is greater than 1/10 but less than 1/3

Step-by-step explanation:

Recall that a probability mass function defined on a discrete random variable X is just a function that gives the probability that the random variable equals a certain value k

In this case we have the event  

“The computer will ask for a roll to the left when a roll to the right is appropriate” with a probability of 0.003.

Then we have 2 possible events, either the computer is right or not.

Since we have 4 computers in parallel, the situation could be modeled with a binomial distribution and the probability mass function

This gives the probability that k computers are wrong at the same time.