SOLUTION: In testing a new drug, researchers found that 20% of all patients using it will have a mild side effect. A random sample of 13 patients using the drug is selected. Find the probabi

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Question 360068: In testing a new drug, researchers found that 20% of all patients using it will have a mild side effect. A random sample of 13 patients using the drug is selected. Find the probability that:

(A) exactly three will have this mild side effect
(B) at least five will have this mild side effect.
Binomial Problem with n=13; p=0.20
Find the probability that exactly three will have this mild side effect
P(x=3)=0.20^3
I am not sure if I am on the right track with this?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

Binomial Problem with n=13; p=0.20  Yes, you are on the right track there.



Note: The probability of x successes in n trials is: 



P = nCx* p%5Ex*q%5E%28n-x%29 where p and q are the probabilities of success and failure respectively.

In this case p(mild side effect)=.2 & q =.8 

nCx = n%21%2F%28x%21%28n-x%21%29%29



(A) exactly three will have this mild side effect

P(3 with mild side effects) = 13C3* .2%5E3*.8%5E10

13C3 = 13!/3!10! = 13*12*11/3*2 = 286

P(3 with mild side effects) = 286* .2%5E3*.8%5E10



(B) at least five will have this mild side effect. 

1-   P(0)   + P(1)       + P(2)             + P(3)         + P(4) 

1 - .8^13 + 13*.2^1.8^12 + 78*.2^2.8^11 + 286*.2^3.8^10 + 715*.2^4.8^9