To find P(X>0), we can use the fundamental property that the sum of all probabilities in a probability distribution must equal 1.
- P(X=0)=81
- 4P(X=4)=81⟹P(X=4)=321
- 3P(X=3)=81⟹P(X=3)=241
The event X>0 includes the outcomes X=1,X=2,X=3, and X=4. The complement of this event is X=0.
The formula for the complement is:
P(X > 0) = 1 - P(X = 0)$ Substituting the known value for $P(X = 0)$:P(X > 0) = 1 - \frac{1}{8}P(X > 0) = \frac{8}{8} - \frac{1}{8}P(X > 0) = \frac{7}{8}$$