SOLUTION: Please help me solve this in simpe way. Thank You. It is known that a certain drug causes side effects in 12% of patients. If we consider a random sampling of 15 patients, what

Question 1119913: Please help me solve this in simpe way. Thank You.
It is known that a certain drug causes side effects in 12% of patients. If we consider a random sampling of 15 patients, what is the probability less than two have the side effect?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
drug causes side effects in 12% of patients.
sample size is 15.
what is probability less than 2 have the side effect.

p = .12
q = 1 - .12 = .88
n = 15

p(x) = p^x * q^(n-x) * c(n,x)

p(0) = .12^0 * .88^15 * c(15,0) = .146974
p(1) = .12^1 * .88^14 * c(15,1) = .300628

p(less than 2) = p(0) + p(1) = .447602

c(n,x) is the number of possible combinations of x elements out of n when order within each set is not important.

the formula is n! / (x! * (n-x)!)

for example, c(15,1) = 15! / (1! * 14!) = (15 * 14!) / (1! * 14!) = 15 / 1 = 15.

also, c(15,0) = 15! / (0! * 15!) = 1 / 0!
0! is equal to 1 by definition, so 1 / 0! = 1 / 1 = 1.

all the probabilities must be equal to 1 or you made a mistake in the calculations.

all of the probabilities are shown in the following excel printout.

$$$

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