Question

An experimental drug has been shown to be 75% effective in eliminating symptoms of allergies in animal studies. A small human study involving six participants is conducted. What is the probability that the drug is effective on half of the participants?

Answer 1

`P(x=3) = 0.1318`

Explanation:

The question illustrates a binomial distribution and the given parameters are:

Given

`n = 6` -- sample size

`p = 0.75` --- probability of success

`r = 3` --- half of the participant

Using the binomial probability formula, we have:

`P_x = ^nC_xp^x(1-p)^(n-x)`

For x = 3, the probability is:

`P(x=3) = ^6C_3*0.75^3 * (1-0.75)^(6-3)`

`P(x=3) = 20*0.75^3 * 0.25^3`

`P(x=3) = 0.1318`