Question

“ group of patients in a blind drug trial is assigned numbers from 1 through 8. The even numbers get an experimental drug, while the odd numbers get a placebo.

a/ If Eleanor is one of the patients, use the conditional probability formula to find the probability that she’s getting the experimental drug given that she wasn’t assigned 1, 2, or 3.

b/ “Compute the same probability by writing out a new sample space and using the theoretical probability formula.

c/ Which method do you prefer? Why?

Answer 1

a.

Probability that she’s getting the experimental drug given that she wasn’t assigned 1, 2, or 3

= Probability that she’s getting the even number AND wasn’t assigned 1, 2, or 3 / Probability that she wasn’t assigned 1, 2, or 3 (By conditional probability formula)

= Probability that she’s assigned 4, 6 or 8 / Probability that she's assigned 4, 5, 6, 7, 8

= (3/8) / (5/8)

= 3/5

b.

Given given that she wasn’t assigned 1, 2, or 3, the new sample space is S = {4, 5, 6, 7, 8}

Sample space that she’s getting the experimental drug (even number) E = {4 , 6, 8}

Probability that she’s getting the experimental drug using the theoretical probability formula

= n(E) / n(S)

= 3/5

c.

The theoretical probability method is preferred as it is easier to compute.