Question 1007965
p(x) = c(n,x) * p^x * q^(n-x)


x = 5
n = 15
p = .5
q = .5


formula becomes:


p(5) = c(15,5) * .5^5 * .5^10


solve for p(5) to get:


p(5) = .0916442871


c(15,5) is the combination formula for the number of ways to select 5 things out of 15 where order doesn't matter.


the general formula is c(n,x) = n! / (x! * (n-x)!)


when n = 15 and x = 5, c(n,x) becomes:


c(15,5) = 15! / (5! * 10!) = (15*14*13*12*11*10!) / (5! * 10!)


this becomes:


c(15,5) = (15*14*13*12*11) / (5*4*3*2*1) which becomes (21*13*11 which is equal to 3003.


c(15,5) * p^x * q^(n-x) becomes 3003 * .5^5 * .5^10 which becomes 3003 * .5^15 which becomes .0916442871


that's the probability of getting exactly 5 heads out of 15 tosses.


the value of n is 15.
the value of x is 5
the value of p is .5


the full probability table for this problem is shown below:


the total probability is equal to 1 as it should be.


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