A pharmaceutical lab states that a drug causes negative side effects in 3 of eve

Question

A pharmaceutical lab states that a drug causes negative side effects in 3 of every 100 patients. To confirm this affirmation, another laboratory chooses 5 people at random who have consumed the drug. What is the probability of the following events? a. None of the five patients experience side effects. (3 points) b. At least two experience side effects. (4 points) c. What is the average number of patients that the laboratory should expect to experience side effects if they choose 100 patients at random? (3 points)

Explanation / Answer

Answer to the questions as below:

p = 3/100 = .03

a. P( none of the 5 patients exp. side effects) =?

= 5C0(.03)^0(.97^5)
= 1*1*.97^5
= .9269

b. P( atleast 2 exp. side effects)
= P(X>=2) = 1-P(X<2)
= 1- P(X=0,1)
= 1- (5C0(.03)^0(.97^5)+5C1(.03)^1(.97^4))
= .1328

c. This is the expected value.
E(X) = np = 100*.03 = 30

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