A-number-is-selected-at-random-from-the-integers-10-to-35-exclussive-such-that-the-chances-take-the-subsets-of-P-Q-and-R-respectively-where-P-is-even-Q-is-even-or-prime-number-and-R-is-odd-prime

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Question Number 11599 by tawa last updated on 28/Mar/17

$$\mathrm{A}\mathrm{number}\mathrm{is}\mathrm{selected}\mathrm{at}\mathrm{random}\mathrm{from}\mathrm{the}\mathrm{integers}10\mathrm{to}35\mathrm{exclussive},\mathrm{such}$$$$\mathrm{that}\mathrm{the}\mathrm{chances}\mathrm{take}\mathrm{the}\mathrm{subsets}\mathrm{of}\mathrm{P},\mathrm{Q}\mathrm{and}\mathrm{R}\mathrm{respectively},\mathrm{where}\mathrm{P}\mathrm{is}$$$$\mathrm{even},\mathrm{Q}\mathrm{is}\mathrm{even}\mathrm{or}\mathrm{prime}\mathrm{number},\mathrm{and}\mathrm{R}\mathrm{is}\mathrm{odd}\mathrm{prime}\mathrm{numbers}.\mathrm{What}\mathrm{is}$$$$\mathrm{the}\mathrm{probability}$$$$\left(\mathrm{a}\right)\mathrm{That}\mathrm{exacly}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{events}\mathrm{of}\mathrm{the}\mathrm{subset}\mathrm{is}\mathrm{choosen}?$$$$\left(\mathrm{b}\right)\mathrm{Of}\mathrm{choosen}\mathrm{at}\mathrm{most}\mathrm{two}\mathrm{of}\mathrm{the}\mathrm{subset}\mathrm{of}\mathrm{the}\mathrm{event}.$$

Answered by mrW1 last updated on 29/Mar/17

$$10,11,\dots ,35\Rightarrow 36pieces$$$$P=(10,12,\dots ,34)\Rightarrow 13pieces$$$$Pr=(11,13,17,19,23,31)\Rightarrow 6pieces$$$$Q=PorPr\Rightarrow 13+6=19pieces$$$$R=Pr\Rightarrow 6pieces$$$$\left(a\right)\frac{6}{36}=16.6\mathrm{\%}$$$$\left(b\right)\frac{13}{36}=36.1\mathrm{\%}$$

Commented by tawa last updated on 29/Mar/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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