P(A)=0.6,P(B)=0.4,P(C)=0.5; P(A B)=0.8, P(A C)=0.3, P(A B C)=0.2, P(B C)=, P(A B C)=, 0.85…

Question

$P(A)=0.6,P(B)=0.4,P(C)=0.5$; $P(A\cup B)=0.8$, $P(A\cap C)=0.3$, $P(A\cap B\cap C)=0.2$, $P(B\cap C)=\beta$, $P(A\cup B\cup C)=\alpha$, $0.85\le\alpha\le0.95$. Find the interval for $\beta$.

Accepted Answer

$P(A\cap B)=P(A)+P(B)-P(A\cup B)=0.2$.

$$\alpha = 0.6+0.4+0.5-0.2-\beta-0.3+0.2 \implies \beta = 1.2-\alpha$$

Since $\alpha\in[0.85,0.95]$, $\beta\in[0.25,0.35]$.

Solutions · 1