Question

24. A patient receiving a medical vaccination has a 93.5% probability of not experiencing side effects. Suppose that this vaccination is given to ten random patients.

a. What is the probability that none of the ten patients will experience side effects?

Round your answer to four decimal places. Probability = ???

b. What is the probability that at least one the ten patients will experience side effects?

Round your answer to four decimal places. Probability = ???

c. Suppose that an improvement is made to the vaccination which increases the probability of no side effects from 93.5% to 95.0%. Compute the revised probability that none of the ten random patients will experience side effects.

Round your answer to four decimal places. Probability = ???

d. Given your answer in Part c, compute the revised probability that at least one the ten random patients will experience side effects.

Round your answer to four decimal places. Probability = ???

Answer 1

here this is binomial with parameter n=10 and p=1-0.935 =0.065

a)

probability =

P(X=0)=

(nCx)px(1−p)(n-x)    =

0.5106

b)

probability =

P(X>=1)=

1-P(X<=0)=

1-∑x=0x-1     (nCx)px(1−p)(n-x)    =

0.4894

c)

here this is binomial with parameter n=10 and p=0.05

probability =

P(X=0)=

(nCx)px(1−p)(n-x)    =

0.5987

d)

probability =

P(X>=1)=

1-P(X<=0)=

1-∑x=0x-1     (nCx)px(1−p)(n-x)    =

0.4013