Question 1120611
probability of choosing mushroom pizza is .35
probability of choosing cheese pizza is 1 - .35 = .65


formula to use is:


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


p is the probability she chooses mushroom pizza on any given night.
q is the probability she chooses cheese pizza on any given night.
n is the total possible nights she gets to choose.
x is the total number of nights she chooses mushroom pizza


the probability she will choose 2 mushroom pizzas in the week gets you:


p(2) = .35^2 * .65^5 * c(7,2)


the probability she will choose 3 gets you:


p(3) = .35^3 * .65^4 * c(7,3)


the probability she will choose 4 gets you:


p(4) = .35^4 * .65^3 * c(7,4)


the probability she chooses mushroom pizza on 2 to 4 night is equal to p(2) + p(3) + p(4).


c(n,x) = n! / (x! * (n-x)!)


for example:


c(7,2) = 7! / (2! * 5!) = (7 * 6 * 5!) / (2! * 5!) = (7 * 6) / (2 * 1) = 42 / 2 = 21.


all the probabilities from 0 to 7 are shown in the following spreadsheet printout.


the total probability is 1 as it should be.


the probability of choosing mushroom pizza on 2 to 4 nights in the week is equal to p(2) + p(3) + p(4) which is equal to 0.710594 as shown in the excel printout.


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