Question

Unknown to a medical researcher, 8 out of 20 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

Let , 'p' be the probability that the patients have a heart problem that will result in death if they receive the test drug.

Therefore , p =8/20=0.40

Let , X be the number of patients have a heart problem that will result in death if they receive the test drug.

Here , X has a binomial distribution with parameter n=5 and p=0.40

Therefore , the probability mass function of X is ,

; x=0,1,2,.........,n and q=1-p

= 0 ; otherwise

Now ,

Therefore , the probability that less than 4 patients will die is 0.9130