Events A,B,C mutually exclusive: P(A)=3x+13, P(B)=1-x4, P(C)=1-2x2.

Question

Events $A,B,C$ mutually exclusive: $P(A)=\dfrac{3x+1}{3}$, $P(B)=\dfrac{1-x}{4}$, $P(C)=\dfrac{1-2x}{2}$. Find the interval for $x$.

Accepted Answer

Combining $0\le P(A)\le1$: $-\dfrac13\le x\le\dfrac23$; $0\le P(B)\le1$: $-3\le x\le1$; $0\le P(C)\le1$: $-\dfrac12\le x\le\dfrac12$; and $P(A)+P(B)+P(C)\le1$: $\dfrac13\le x\le\dfrac{13}{3}$.

Intersection: $x\in\left[\dfrac13,\dfrac12\right]$.

Solutions · 1