1. The probability of an adverse reaction to a pneumonia shot is 0.20. Pneumonia

Question

1. The probability of an adverse reaction to a pneumonia shot is 0.20. Pneumonia shots are given to a group of 12 people. What is the probability that none of them will have an adverse reaction to the pneumonia shot?

2. What is the probability that more than half of them will have an adverse reaction to the pneumonia shot?

3. What is the probability that 1 or fewer of the 12 people will have an adverse reaction to the pneumonia shot?

4. What is the probability that two or more of the 12 people will have an adverse reaction to the pneumonia shot?

Explanation / Answer

Answer to the question is as follows:

1.What is the probability that none of them will have an adverse reaction to the pneumonia shot?

p(penu) = .20

Lets use the binomial pdf function : P(n,x) = nCx * p^x * (1-p)*(n-x)

P(X=0) = 12C0*.2^12*.8^0 = .41*10^-9

2. What is the probability that more than half of them will have an adverse reaction to the pneumonia shot?

P(X>6) = P(X=7,8,9,10,11,12) = 0.0039

3. P(X<=1) =P(X=0,1) =0.2749

4. P(X>=2) =1 -P(X<=1) = 0.7251

3. What is the probability that 1 or fewer of the 12 people will have an adverse reaction to the pneumonia shot?

4. What is the probability that two or more of the 12 people will have an adverse reaction to the pneumonia shot?

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