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

Answer:

$P(x=3) = 0.1318$

Step-by-step 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:

$P(x=3) = ^6C_3*0.75^3 * (1-0.75)^{6-3}$

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

$P(x=3) = 0.1318$