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Question Number 145869 by Ar Brandon last updated on 09/Jul/21
$$\mathrm{Let}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{be}\:\mathrm{2}\:\mathrm{events}\:\mathrm{such}\:\mathrm{that}\:\mathrm{P}\left(\mathrm{A}\right)=\mathrm{0}.\mathrm{4},\:\mathrm{P}\left(\overset{−} {\mathrm{B}}/\mathrm{A}\right)=\mathrm{0}.\mathrm{7} \\ $$$$\:\mathrm{and}\:\mathrm{P}\left(\mathrm{B}/\overset{−} {\mathrm{A}}\right)=\mathrm{0}.\mathrm{6},\:\mathrm{then}\:\mathrm{find} \\ $$$$\left({i}\right)\mathrm{P}\left(\overset{−} {\mathrm{B}}/\overset{−} {\mathrm{A}}\right)\:\:\left({ii}\right)\mathrm{P}\left(\mathrm{A}\cap\mathrm{B}\right)\:\:\:\left({iii}\right)\:\mathrm{P}\left(\mathrm{B}\right)\:\:\left({iv}\right)\mathrm{P}\left(\mathrm{A}\cup\mathrm{B}\right) \\ $$
Answered by gsk2684 last updated on 09/Jul/21
$${using}\:{multiplication}\:{theorem}\: \\ $$$${P}\left({A}\cap\overset{−} {{B}}\right)=\mathrm{0}.\mathrm{4}×\mathrm{0}.\mathrm{7} \\ $$$$\Rightarrow{P}\left({A}\right)−{P}\left({A}\cap{B}\right)=\mathrm{0}.\mathrm{28} \\ $$$$\Rightarrow{P}\left({A}\cap{B}\right)=\mathrm{0}.\mathrm{4}−\mathrm{0}.\mathrm{28}=\mathrm{0}.\mathrm{12} \\ $$$$\&\:{P}\left({B}\cap\overset{−} {{A}}\right)=\mathrm{0}.\mathrm{6}×\mathrm{0}.\mathrm{6} \\ $$$$\Rightarrow{P}\left({B}\right)−{P}\left({B}\cap{A}\right)=\mathrm{0}.\mathrm{36} \\ $$$$\Rightarrow{P}\left({B}\right)=\mathrm{0}.\mathrm{36}+\mathrm{0}.\mathrm{12}=\mathrm{0}.\mathrm{48} \\ $$$${proceed}\:{with}\:{these} \\ $$$$ \\ $$
Commented by Ar Brandon last updated on 09/Jul/21
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{Sir} \\ $$
Answered by bramlexs22 last updated on 09/Jul/21
Commented by Ar Brandon last updated on 09/Jul/21
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{Sir} \\ $$