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Category: Probability and Statistics

What-is-the-probability-that-in-a-class-of-18-people-there-exists-a-group-of-3-people-born-on-the-same-day-of-the-week-

Question Number 199310 by necx122 last updated on 01/Nov/23 $${What}\:{is}\:{the}\:{probability}\:{that}\:{in}\:{a}\:{class}\: \\ $$$${of}\:\mathrm{18}\:{people},\:{there}\:{exists}\:{a}\:{group}\:{of}\:\mathrm{3} \\ $$$${people}\:{born}\:{on}\:{the}\:{same}\:{day}\:{of}\:{the} \\ $$$${week}? \\ $$ Commented by AST last updated on 01/Nov/23…

60-students-of-a-school-must-take-at-least-one-of-the-three-courses-for-mathematics-physics-and-chemistry-respectively-if-a-student-is-randomly-picked-what-is-the-probability-that-he-she-takes-only

Question Number 198975 by mr W last updated on 26/Oct/23 $$\mathrm{60}\:{students}\:{of}\:{a}\:{school}\:{must}\:{take} \\ $$$${at}\:{least}\:{one}\:{of}\:{the}\:{three}\:{courses}\:{for} \\ $$$${mathematics},\:{physics}\:{and}\:{chemistry} \\ $$$${respectively}. \\ $$$${if}\:{a}\:{student}\:{is}\:{randomly}\:{picked},\:{what} \\ $$$${is}\:{the}\:{probability}\:{that}\:{he}/{she}\:{takes} \\ $$$${only}\:{one}\:{course}? \\ $$…

1-0-x-1-x-sin-pix-dx-

Question Number 198141 by Erico last updated on 11/Oct/23 $$\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \:\frac{\mathrm{x}\left(\mathrm{1}−\mathrm{x}\right)}{\mathrm{sin}\left(\pi\mathrm{x}\right)}\mathrm{dx}=??? \\ $$ Answered by witcher3 last updated on 11/Oct/23 $$\frac{\mathrm{1}}{\mathrm{sin}\left(\pi\mathrm{x}\right)}=\frac{\mathrm{2ie}^{−\mathrm{i}\pi\mathrm{x}} }{\mathrm{1}−\mathrm{e}^{−\mathrm{2i}\pi\mathrm{x}} }\: \\…

A-research-station-supplies-three-varieties-of-seeds-S1-S2-and-S3-in-the-ratio-4-2-1-The-probabilities-of-germination-of-S1-S2-and-S3-are-50-60-and-80-respectively-Find-the-probability-tha

Question Number 194490 by pete last updated on 08/Jul/23 $$\mathrm{A}\:\mathrm{research}\:\mathrm{station}\:\mathrm{supplies}\:\mathrm{three}\:\mathrm{varieties}\: \\ $$$$\mathrm{of}\:\mathrm{seeds}\:\mathrm{S1},\:\mathrm{S2}\:\mathrm{and}\:\mathrm{S3}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{4}:\:\mathrm{2}:\:\mathrm{1}. \\ $$$$\mathrm{The}\:\mathrm{probabilities}\:\mathrm{of}\:\mathrm{germination}\:\mathrm{of}\: \\ $$$$\mathrm{S1},\:\mathrm{S2}\:\mathrm{and}\:\mathrm{S3}\:\mathrm{are}\:\mathrm{50\%},\:\mathrm{60\%}\:\mathrm{and}\:\mathrm{80\%} \\ $$$$\mathrm{respectively}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{a}\:\mathrm{seed}\:\mathrm{selected}\:\mathrm{at}\:\mathrm{random}\:\mathrm{will}\:\mathrm{germinate}. \\ $$ Answered by MM42…