p p  =  3p2q
and
P(X = 3) = P(three success) = P ({SSS})
= P(S) P(S) P(S) = p3
Thus, the probability distribution of X is
X
0
1
2
3
P(X)
q 3
3q2p
3qp2
p 3
Also, the binominal expansion of (q + p)3 is
q
q
p
qp
p
3
3 2
3
2
3
+
+
+
Note that the probabilities of 0, 1, 2 or 3 successes are respectively the 1st, 2nd,
3rd and 4th term in the expansion of (q + p)3