Events $A$ and $B$are such that $P(A)=0.7$and $P(B)=0.8$. Show that \(P(A\cap B)\ge 0.5

Question

Events $A$ and $B$are such that $P(A)=0.7$and $P(B)=0.8$. Show that $P(A\cap B)\ge 0.5$[2] If $\mathrm{P}(A'\cup B)=0.85$, find $\mathrm{P}(A\,\left| B \right.)$. State, with a reason, whether or not $A$and $B$are independent events.[3] What is the relationship between event $A$ and event $B$ if $\mathrm{P}(A\cap B)=0.5$?[1] Eleven non-parallel lines are drawn in a plane. If no three lines intersect at a common point, show that there are $55$ points of intersection between the lines. If three of these points are chosen at random, find the probability that they are all on one of the eleven lines.[4]

Accepted Answer

(a)(i) $P(A\mid B)=\frac{11}{16}$, not independent (a)(ii) Exhaustive (b) $\frac{8}{159}$

2012 AJC P2 Q7

2012 AJC P2 Q7

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