This is a binomial distribution because there are only 2 outcomes (the patient dies, or does not).
Let X = number who recover.
Here, n = 6 and x = 4. Let p = 0.25 (success - i.e. they live), q = 0.75 (failure, i.e. they die).
The probability that 4 will recover:
We could calculate all the probabilities involved and we would get:
The histogram (using Excel) is as follows:
It means that out of the 6 patients chosen, the probability that none of them will recover is 0.17798, the probability that one will recover is 0.35596, and the probability that all 6 will recover is extremely small.
Alternatively, we can use Scientific Notebook's "Plot Approximate Integral" to give us something approaching the histogram of this experiment. Of course, the x-values are not quite right in the SNB answer (because it was not designed to do this), so I have made an adjustment to the x-axis.
