Question

OaestiOnEO O1 25 312D1 O 59:33:15 Unknown to a medical researcher, 7 out of 17 patients have a heart problem that will result in death if they receive the test drug. 5 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that less than 4 patients will die? Express your answer as a fraction or a decimal number rounded to four decimal places

Answer 1

Solution:

P(patients have heart problem) = 7/17

P(patients don't have heart problem) = 10/17

No. Of sample = 5

P(X<4) = P(X=0) +P(X=1) +P(X=2)+P(X=3)

= 5C0*(7/17)^0*(10/17)^5 +5C1*(7/17)^1*(10/17)^4+5C2*(7/17)^2*(10/17)^3+5C3*(7/17)^3*(10/17)^2 = 0.0704+0.2465+0.3451+0.2416 = 0.9036