Given Binomal $\displaystyle A=(3,\frac{1}{6})$
and $\displaystyle B=Geo(0.5)$
Find $\displaystyle P(A=B)$
Thanks!
If you find the binomial distribution in question to be
x P(A=x)
0 125/216
1 75/216
2 15/216
3 1/216
and the geometric distribution in question to be
x P(B=x)
1 1/2
2 1/4
3 1/8
...
and we assume the two variables to be independent and random
then we can find the probability that A=B
by summing over x= 1,2 and 3
P(A=x) * P(B=x)
as B cannot = 0 and A cannot be > 3
ie
= 75/216 * 1/2 + 15/216 * 1/4 + 1/216 * 1/8 = 331/1728