Question Number 182695 by cortano1 last updated on 13/Dec/22
$$\:\:\mathrm{If}\:\mathrm{two}\:\mathrm{events}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{such}\: \\ $$$$\:\:\mathrm{that}\:\mathrm{P}\left(\mathrm{A}^{\mathrm{c}} \right)=\mathrm{0}.\mathrm{3}\:;\:\mathrm{P}\left(\mathrm{B}\right)=\mathrm{0}.\mathrm{4}\:\mathrm{and} \\ $$$$\:\:\mathrm{P}\left(\mathrm{A}\cap\mathrm{B}^{\mathrm{c}} \right)=\:\mathrm{0}.\mathrm{5}\:\mathrm{then}\:\mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}\cup\mathrm{B}^{\mathrm{c}} }\right)=? \\ $$$$\:\left(\mathrm{A}\right)\:\mathrm{0}.\mathrm{20}\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{0}.\mathrm{25}\:\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{0}.\mathrm{30}\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{0}.\mathrm{35} \\ $$$$\:\: \\ $$
Commented by Acem last updated on 13/Dec/22
$${Hi}\:{friend}! \\ $$$${What}\:{does}\:{A}\:^{{c}} \:{mean}? \\ $$
Commented by Emrice last updated on 13/Dec/22
$$ \\ $$it is the conditional probability. and in our case here it is the probability of A knowing C.
Answered by greougoury555 last updated on 14/Dec/22
$$\:{P}\left({B}/{A}\cup\overline {{B}}\right)=\:\frac{{P}\left({A}\cap{B}\right)}{{P}\left({A}\cup\overline {{B}}\:\right)} \\ $$$$\:=\:\frac{\mathrm{0}.\mathrm{7}−\mathrm{0}.\mathrm{5}}{\mathrm{0}.\mathrm{7}+\mathrm{0}.\mathrm{6}−\mathrm{0}.\mathrm{5}}\:=\:\frac{\mathrm{0}.\mathrm{2}}{\mathrm{0}.\mathrm{8}}\:=\:\mathrm{0}.\mathrm{25} \\ $$