Answer: 0.4
Step-by-step explanation:
The probability of X>=4 given X >=1 can be written:
Let A be X>=4.
Let B be X>=1.
The probability that A given B, P(A|B) equals...
P(A and B) / P(B).
So we need P(A and B) and P(B). P(A and B) is the same as P(A), since all X>=4 are also >=1.
Let's make a chart.
x f(x)
0 1([0]+1) - 1/([0] + 2) = .5
1 1([1]+1) - 1/([1] + 2) = .16667
2 1([2]+1) - 1/([2] + 2) = .08333
3 1([3]+1) - 1/([3] + 2) = .05
4 1([4]+1) - 1/([4] + 2) = .03333
5 1([5]+1) - 1/([5] + 2) = .02381
A is the P(X>=4), which is the complement of P(X<3).
P(X<3) = P(X=0) + P(X=1) + P(X=2) + P(X=3) = .5 +.16667 + .08333 + .05 = .8. The complement = 1 - 0.8 = 0.2
B is the P(X>=1), which is the same as complement of P(X=0). 1-P(X=0) = 1-0.5 = 0.5
P(A) = 0.2 = 1/5
P(B) = .5 = 1/2
P(A|B) = 1/5 / 1/2 = 0.4
