Let X = number of rejected pistons

(In this case, "success" means rejection!)

Here, n = 10, p = 0.12, q = 0.88.

(a)

No rejects

One reject

Two rejects

So the probability of getting no more than 2 rejects is:

(b) We could work out all the cases for X = 2, 3, 4, ..., 10, but it is much easier to proceed as follows:

Histogram

Using SNB , we can define the function and then use matrices to find the values at 0, 1, 2, ... which gives us the histogram:

Alternatively, using SNB :