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, that is, they live), `q = 0.75` (failure, i.e. they die).

The probability that `4` will recover:

`P(X)` `= C_x^np^xq^[n-x]` `=C_4^6(0.25)^4(0.75)^2` `=15times 2.1973 times 10^-3` `=0.0329595 `

Histogram of this distribution:

We could calculate all the probabilities involved and we would get:

`X``text[Probability]`
`0``0.17798`
`1``0.35596`
`2``0.29663`
`3``0.13184`
`4``3.2959 times 10^-2`
`5``4.3945times10^-3`
`6``2.4414times10^-4`

The histogram (using Excel) is as follows:

Probabilities of death

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.

SNB "Histogram"

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.


Probability death histogram