n = 12
x = 5
p = .7
q = 1 - .7 = .3
p is probability of success
q is probability of failure
p(x) = nCx * p^x * q^(n-x)
for x = 5 and n = 12, this becomes:
p(5) = 12C5 * (.7)^5 * (.3)^7 which becomes:
p(5) = 792 * .16807 * .0002187 which becomes:
p(5) = .029111472
nCx is the combination formula of n! / (x! * (n-x)!))
the probabilities for x = 1 to x = 12 are shown below.
p 0.7
q 0.3
n 12
x p(x)
0 5.31441E-07
1 1.48803E-05
2 0.000190964
3 0.001485279
4 0.007797716
5 0.029111472 ***** p(x = 5)
6 0.079247896
7 0.158495792
8 0.231139696
9 0.239700426
10 0.167790298
11 0.071183763
12 0.013841287
1 total probability equals 1 (as it should)
this should be approximately equal to the probability found in your textbook.
if not, let me know what is in table 2 of appendix b in your notebook.