SOLUTION: Can someone PLEASE HELP!!! Suppose we want to determine the (binomial) probability (p) of getting 5 heads in 15 flips of a 2-sided coin. Using the Binomial table in the appendi

Question 1007965: Can someone PLEASE HELP!!!
Suppose we want to determine the (binomial) probability (p) of getting 5 heads in 15 flips of a 2-sided coin. Using the Binomial table in the appendix of the text, what values of n, x, and p would we use to look up this probability, and what would be the probability?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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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