Question

If $P\left(A\right)=0.65,P\left(B\right)=0.80,$ then $P(A\cap B)$lies in the interval:

• A. $[0.30,0.80]$
• B. $[0.35,0.75$]
• C. $[0.4,0.70$]
• D. $[0.45,0.65]$

Answer 1

Answer: (D)

$[0.45,0.65]$

$P\left(A\cap B\right)⩽min\left(P\right(A),P(B\left)\right)$

$min(0.65,0.80)$

$0.65$

$P(A\cap B)=P\left(A\right)+P\left(B\right)-P(A\cup B)$

$\ge 0.65+0.80-1$

$\ge 0.45$

$0.45\le P(A\cap B)\le 0.65$

$P(A\cap B)=\left[0.45,0.65\right]$