If-A-and-B-are-two-indpendent-events-the-probability-that-both-A-and-B-occur-is-1-8-and-the-probability-that-neither-of-them-occurs-is-3-8-The-probability-of-the-occurrence-of-A-is-

Question Number 81925 by zainal tanjung last updated on 16/Feb/20

$$\mathrm{If}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{indpendent}\:\mathrm{events}, \\ $$$$\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{both}\:{A}\:\mathrm{and}\:{B}\:\mathrm{occur} \\ $$$$\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{8}}\:\mathrm{and}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{neither}\:\mathrm{of} \\ $$$$\mathrm{them}\:\mathrm{occurs}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{8}}\:.\:\mathrm{The}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{occurrence}\:\mathrm{of}\:{A}\:\mathrm{is} \\ $$

Answered by MJS last updated on 16/Feb/20

$$\mathrm{both}:\:{ab}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$$$\mathrm{neither}:\:\left(\mathrm{1}−{a}\right)\left(\mathrm{1}−{b}\right)=\frac{\mathrm{3}}{\mathrm{8}} \\ $$$$\Rightarrow\:{a}=\frac{\mathrm{1}}{\mathrm{2}}\wedge{b}=\frac{\mathrm{1}}{\mathrm{4}}\:\vee\:{a}=\frac{\mathrm{1}}{\mathrm{4}}\wedge{b}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

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