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Category: Probability and Statistics

Question-124376

Question Number 124376 by bemath last updated on 02/Dec/20 Answered by liberty last updated on 02/Dec/20 $${n}\left({A}\right)=\:{C}_{\mathrm{1}} ^{\:\mathrm{10}} \:=\:\mathrm{10} \\ $$$${n}\left({S}\right)\:=\:{C}\:_{\mathrm{2}} ^{\mathrm{20}} \:=\:\frac{\mathrm{20}×\mathrm{19}}{\mathrm{2}×\mathrm{1}}\:=\:\mathrm{190}\: \\ $$$${p}\left({A}\right)\:=\:\frac{\mathrm{10}}{\mathrm{190}}\:=\:\frac{\mathrm{1}}{\mathrm{19}}.…

Question-124282

Question Number 124282 by bramlexs22 last updated on 02/Dec/20 Answered by liberty last updated on 02/Dec/20 Commented by malwan last updated on 02/Dec/20 $$\frac{\begin{pmatrix}{\mathrm{5}}\\{\mathrm{5}}\end{pmatrix}}{\begin{pmatrix}{\mathrm{25}}\\{\mathrm{5}}\end{pmatrix}}\:=\:\frac{\mathrm{1}}{\frac{\mathrm{25}×\mathrm{24}×\mathrm{23}×\mathrm{22}×\mathrm{21}}{\mathrm{5}×\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}}}\: \\…

A-man-has-equal-chances-of-travelling-by-air-A-bus-B-and-train-T-the-probability-that-when-he-travels-by-air-bus-or-train-he-will-have-an-accident-are-1-3-3-5-and-1-10-find-the-probab

Question Number 189641 by MikeH last updated on 19/Mar/23 $$\mathrm{A}\:\mathrm{man}\:\mathrm{has}\:\mathrm{equal}\:\mathrm{chances}\:\mathrm{of}\:\mathrm{travelling}\:\mathrm{by}\: \\ $$$$\mathrm{air}\left(\mathrm{A}\right),\:\mathrm{bus}\left(\mathrm{B}\right)\:\mathrm{and}\:\mathrm{train}\left(\mathrm{T}\right).\:\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{when}\:\mathrm{he}\:\mathrm{travels}\:\mathrm{by}\:\mathrm{air},\:\mathrm{bus}\:\mathrm{or}\:\mathrm{train}\:\mathrm{he} \\ $$$$\mathrm{will}\:\mathrm{have}\:\mathrm{an}\:\mathrm{accident}\:\mathrm{are}\:\frac{\mathrm{1}}{\mathrm{3}},\:\frac{\mathrm{3}}{\mathrm{5}}\:\mathrm{and}\:\frac{\mathrm{1}}{\mathrm{10}}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{he}\:\mathrm{travelled}\:\mathrm{and}\:\mathrm{was}\:\mathrm{involved}\:\mathrm{in}\:\mathrm{an}\:\mathrm{accident} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{he}\:\mathrm{was}\:\mathrm{travelling}\:\mathrm{by}\:\mathrm{air}\:\mathrm{given}\:\mathrm{that}\:\mathrm{he}\:\mathrm{was} \\ $$$$\mathrm{involved}\:\mathrm{in}\:\mathrm{an}\:\mathrm{accident}. \\…

There-are-100-150-and-250-students-in-forms-one-two-and-three-respectively-in-a-school-If-the-mean-ages-of-tbe-students-in-the-forms-are-15-6-years-16-8-years-and-18years-respectively-find-i-th

Question Number 58253 by pete last updated on 20/Apr/19 $$\mathrm{There}\:\mathrm{are}\:\mathrm{100},\:\mathrm{150}\:\mathrm{and}\:\mathrm{250}\:\mathrm{students}\:\mathrm{in} \\ $$$$\mathrm{forms}\:\mathrm{one},\:\mathrm{two}\:\mathrm{and}\:\mathrm{three},\:\mathrm{respectively} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{school}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{ages}\:\mathrm{of}\:\mathrm{tbe}\:\mathrm{students}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{forms}\:\mathrm{are}\:\mathrm{15}.\mathrm{6}\:\mathrm{years},\:\mathrm{16}.\mathrm{8}\:\mathrm{years}\:\mathrm{and} \\ $$$$\mathrm{18years}\:\mathrm{respectively},\:\mathrm{find} \\ $$$$\mathrm{i}.\:\mathrm{the}\:\mathrm{total}\:\mathrm{number}\:\mathrm{of}\:\mathrm{students}\:\mathrm{in}\:\mathrm{the}\:\mathrm{forms} \\ $$$$\mathrm{ii}.\:\mathrm{correct}\:\mathrm{to}\:\mathrm{one}\:\mathrm{decimal}\:\mathrm{place},\:\mathrm{the}\:\mathrm{mean} \\ $$$$\mathrm{age}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{students} \\…

Question-123771

Question Number 123771 by benjo_mathlover last updated on 28/Nov/20 Commented by benjo_mathlover last updated on 28/Nov/20 $$\:{let}\:\blacklozenge\:=\:{man}\:,\:\heartsuit={woman} \\ $$$$\:\blacklozenge\heartsuit\blacklozenge\heartsuit\blacklozenge\heartsuit\blacklozenge\heartsuit\blacklozenge\heartsuit\blacklozenge\heartsuit\blacklozenge= \\ $$$$\:\mathrm{3}!\:×{C}_{\mathrm{3}} ^{\mathrm{6}} ×\mathrm{5}!\:×\mathrm{42} \\ $$$${p}\left({A}\right)=\:\frac{\mathrm{3}!×{C}_{\mathrm{3}}…