n | Binomial | Expanded Binomial | ||
---|---|---|---|---|
1 | (a + b)1 |
a + b | ||
2 | (a + b)2 |
a2 + 2ab + b2 | ||
3 | (a + b)3 |
a3 + 3a2b + 3ab2 + b3 | ||
4 | (a + b)4 |
a4 + 4a3b + 6a2b2 + 4ab3 +
b4 | ||
5 | (a + b)5 |
a5 +
5a4b +
10a3b2 +
10a2b3 +
5ab4 +
b5 | ||
For example, what is the probability (p) of having two boys and two girls in a family? Let a and b be the probability of having a boy (1/2) and a girl (1/2), respectively. For n = 4, use 6a2b2 in the expanded term.
p = 6a2b2 = 6(1/2)2(1/2)2 = 6(1/2)4 = 6(1/16) = 6/16 = 3/8