Question

If a and b are equally likely events and we require that the probability of their intersection be at least .98, what is p(

Answer 1

If A and B are equally likely events such that the probability of their intersection be at least 0.98, than we can find P(A) as follows;

We know by DeMorgan's law we have,

$\\ P(A\cap B)=1-P(\overline{A\cap B})\\ = 1-P(\overline{A}\cap \overline{B})\\ \text{Since,} P(\overline{A}\cap \overline{B})\leq P(\overline{A})+P(\overline{B}), P(A\cap B)\geq 1-P(\overline{A})-P(\overline{B})\\ \text{we know that,}P(\overline{A})=P(\overline{B})\text{, than we have;}\\ P(A\cap B)\geq 1-2P(\overline{A})\geq 0.98\\ \Rightarrow P(A)\geq 0.99$