Question 945652
  
Given
{{{P(X)=0.5-(X/6)}}} with X∈{0,1,2}
  
Find
1. P(X≥1)
2. P(X≤1)
3. P(1)
  
Solution
  
Using the given probability distribution, we find
P(0) = {{{0.5-0/6 = 1/2}}}
P(1) = {{{0.5-1/6 = 1/3}}}
P(2) = {{{0.5-2/6 = 1/6}}}
from which we check ΣP(X)={{{1/2+1/3+1/6 = 1}}} checks.
  
Since the probabilities are mutually exclusive, we can apply the addition rule:
1. P(X≥1) = {{{P(1)+P(2) = 1/2}}}
2. P(X≤1) = {{{P(0)+P(1) = 5/6}}}
3. P(1) = {{{1/3}}}