Question Number 21580 by ketto last updated on 28/Sep/17
Answered by Joel577 last updated on 29/Sep/17
$$\mathrm{Because}\:{A}\:\mathrm{and}\:{B}\:\mathrm{mutually}\:\mathrm{exclusive},\:\mathrm{then} \\ $$$${P}\:\left({A}\:\cap\:{B}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{and} \\ $$$${P}\:\left({A}\:\cup\:{B}\right)\:=\:\mathrm{1} \\ $$$$ \\ $$$${P}\:\left({A}\:\cup\:{B}\right)\:=\:{P}\:\left({A}\right)\:+\:{P}\:\left({B}\right)\:−\:{P}\:\left({A}\:\cap\:{B}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{1}\:=\:\frac{\mathrm{3}}{\mathrm{7}}\:+\:{P}\:\left({B}\right)\:−\:\mathrm{0} \\ $$$${P}\:\left({B}\right)\:=\:\frac{\mathrm{4}}{\mathrm{7}} \\ $$