Question 1150331
<br>
For each patient,
P(allergic) = 0.20
P(not allergic) = 0.80<br>
Then<br>
P(n of 8 are allergic) = {{{(C(8,n))*((0.20)^n)*((0.80)^(8-n))}}}<br>
Between the four questions that are asked, you need to calculate the probability that nearly any number of the eight are allergic.  So you might as well calculate all the probabilities and verify that their sum is 1; that will give you some reassurance that you have made all the calculations correctly.<br>
a. 3 of 8 allergic<br>
{{{(C(8,3))*((0.20)^3)*((0.80)^(5)) = (56)(.008)(.32768) = 0.14680064}}}<br>
You can do the others....<br>