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Question Number 11266 by ketto last updated on 18/Mar/17

Commented by tawa last updated on 19/Mar/17

probability that juma pass = 50% = (1/2) probability that juma fail = 1 − (1/2) = (1/2) probability that gidi fail = (1/4) probability that gidi pass = 1 − (1/4) = (3/4) (i) probabilty that gidi will pass means that, gidi pass and juma fails = (3/4) × (1/2) = (3/8) (ii) Either juma will pass the examination or gidi will fail the examination = (1/2) + (1/4) = ((2 + 1)/4) = (3/4)

$$\mathrm{probability}\:\mathrm{that}\:\mathrm{juma}\:\mathrm{pass}\:=\:\mathrm{50\%}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{juma}\:\mathrm{fail}\:=\:\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{2}}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{gidi}\:\mathrm{fail}\:=\:\frac{\mathrm{1}}{\mathrm{4}}\: \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{gidi}\:\mathrm{pass}\:=\:\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{4}}\:=\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\left(\mathrm{i}\right) \\ $$$$\mathrm{probabilty}\:\mathrm{that}\:\mathrm{gidi}\:\mathrm{will}\:\mathrm{pass}\:\mathrm{means}\:\mathrm{that},\:\mathrm{gidi}\:\mathrm{pass}\:\mathrm{and}\:\mathrm{juma}\:\mathrm{fails} \\ $$$$=\:\frac{\mathrm{3}}{\mathrm{4}}\:×\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$=\:\frac{\mathrm{3}}{\mathrm{8}} \\ $$$$\left(\mathrm{ii}\right) \\ $$$$\mathrm{Either}\:\mathrm{juma}\:\mathrm{will}\:\mathrm{pass}\:\mathrm{the}\:\mathrm{examination}\:\mathrm{or}\:\mathrm{gidi}\:\mathrm{will}\:\mathrm{fail}\:\mathrm{the}\:\mathrm{examination} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$=\:\frac{\mathrm{2}\:+\:\mathrm{1}}{\mathrm{4}} \\ $$$$=\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$

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