the formula for p(x) = c(n,x) * p^x * q^(n-x)
c(n,x) is the number of ways you can get sets of x out of sets of n where order within the set is not required.
p is the probability of occurrence.
q is the 1 minus the probability of occurence.
x is the number of successes you want out of n tries.
n is the total number of possible tries.
in your problem, you would have.
c(n,x) = c(5,2) which is the possible number of sets of 2 elements you can get out of a set of 5 elements where order is not important.
p = .5 because the probability of getting a head on a single flip of the coin is .5.
q = 1 minus .5 = .5 which is the probability of NOT getting a head on a single flip of the coin.
x is equal to 2 which is the number of times out of 5 that you want to flip a head.
n is equal to 5 which is the total number of times you are flipping the coin.
in your problem, the general equation of p(x) = c(n,x) * p^x * q^(n-x) becomes:
p(2) = c(5,2) * .5^2 * .5^3
work this out and you get p(2) = .3125
to find this in the table, you would look for the table that has n = 5 and you would look for the row that has 2 in it and then you would look for the column that has .5 in it.
the answer shown in the table that i used is the same at .3125.
this is the best and most complete table i could find on the web.
hopefully your table is constructed in a similar mnner.
this table is good because it has multiple tables with n = 1 to n = 29.
it can be found here:
http://www.pindling.org/Math/Statistics/Textbook/Functions/Binomial/binomial_2_8.htm
here's a picture of the table that i used with the correct selection made.
the particular page i selected was on the top row which said n = 2 to 8.
i then found the table with n = 5 and looked for the row with x = 2 and then found the corresponding column with p = .5.
the intersection of the row with x = 2 on it and the column with p = .5 on it gave me the result of .3125.
this is exactly what i manually calculated.
there are also calculators on the web you can use to get the binomial probability.
one such calculator can be found here.
http://stattrek.com/online-calculator/binomial.aspx
for your problem, you would give it probability of success on a single trial is .5 and number of trials is 5 and number of successes is 2.
it will tell you that the probabilility of getting 2 successes out of 5 trials is .3125, same as the table.
it also tells you all sorts of other things about the probability of 2 out of 5 that you might want to know, such as the probabilility of getting less than 2 successes, less than or equal, more than, etc.
this is a great calculator to use to check your work, but don't cheat, since the calculator will more then likely not be at your disposal when you take a test in class.
for your infomation, the frmula of c(n,x) is:
c(n,x) = n! / (x! * (n-x)!)
c(5,2) would be equal to 5! / (2! * 3!) which would be equal to:
5 * 4 * 3 * 2 * 1
----------------------------
2 * 1 * 3 * 2 * 1
you wind up with c(5,2) = 10