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Question Number 136375 by nadovic last updated on 22/Mar/21

A bowl contains carefully shredded confetti, 6 of which are blue and the remaining 12 are red. Each piece of confetti is either circular triangular or rectangular in shape and are in the ratio 1:3:2 for each colour respectively. If they are thrown up thrice in a certain competition and a contestant picks one at random on each throw, what is the probability that he picks a_ (a) different shape on each throw?_ (b) triangular piece which is red in colour on the second throw?_ (c) blue piece of confetti at least twice?

$$\mathrm{A}\:\mathrm{bowl}\:\mathrm{contains}\:\mathrm{carefully}\:\mathrm{shredded} \\ $$$$\mathrm{confetti},\:\mathrm{6}\:\mathrm{of}\:\mathrm{which}\:\mathrm{are}\:\mathrm{blue}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{remaining}\:\mathrm{12}\:\mathrm{are}\:\mathrm{red}. \\ $$$$\mathrm{Each}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{confetti}\:\mathrm{is}\:\mathrm{either}\:\mathrm{circular} \\ $$$$\mathrm{triangular}\:\mathrm{or}\:\mathrm{rectangular}\:\mathrm{in}\:\mathrm{shape}\:\mathrm{and} \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{1}:\mathrm{3}:\mathrm{2}\:\mathrm{for}\:\mathrm{each}\:\mathrm{colour} \\ $$$$\mathrm{respectively}.\:\mathrm{If}\:\mathrm{they}\:\mathrm{are}\:\mathrm{thrown}\:\mathrm{up}\: \\ $$$$\boldsymbol{\mathrm{thrice}}\:\mathrm{in}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{competition}\:\mathrm{and}\:\mathrm{a} \\ $$$$\mathrm{contestant}\:\mathrm{picks}\:\mathrm{one}\:\mathrm{at}\:\mathrm{random}\:\mathrm{on} \\ $$$$\mathrm{each}\:\mathrm{throw},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{he}\:\mathrm{picks}\:\mathrm{a}_{} \\ $$$$\:\:\left({a}\right)\:\mathrm{different}\:\mathrm{shape}\:\mathrm{on}\:\mathrm{each}\:\mathrm{throw}?_{} \\ $$$$\:\:\left({b}\right)\:\mathrm{triangular}\:\mathrm{piece}\:\mathrm{which}\:\mathrm{is}\:\mathrm{red}\:\mathrm{in} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{colour}\:\mathrm{on}\:\mathrm{the}\:\mathrm{second}\:\mathrm{throw}?_{} \\ $$$$\:\:\left({c}\right)\:\mathrm{blue}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{confetti}\:\mathrm{at}\:\mathrm{least} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{twice}? \\ $$

Commented by nadovic last updated on 24/Mar/21

A bowl contains carefully shredded confetti, 6 of which are blue and the remaining 12 are red. Each piece of confetti is either circular triangular or rectangular in shape and are in the ratio 1:3:2 for each colour respectively. If they are thrown up thrice in a certain competition and a contestant picks one at random on each throw, what is the probability that he picks a_ (a) different shape on each throw?_ (b) triangular piece which is red in colour on the second throw?_ (c) blue piece of confetti at least twice?

$$\mathrm{A}\:\mathrm{bowl}\:\mathrm{contains}\:\mathrm{carefully}\:\mathrm{shredded} \\ $$$$\mathrm{confetti},\:\mathrm{6}\:\mathrm{of}\:\mathrm{which}\:\mathrm{are}\:\mathrm{blue}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{remaining}\:\mathrm{12}\:\mathrm{are}\:\mathrm{red}. \\ $$$$\mathrm{Each}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{confetti}\:\mathrm{is}\:\mathrm{either}\:\mathrm{circular} \\ $$$$\mathrm{triangular}\:\mathrm{or}\:\mathrm{rectangular}\:\mathrm{in}\:\mathrm{shape}\:\mathrm{and} \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{1}:\mathrm{3}:\mathrm{2}\:\mathrm{for}\:\mathrm{each}\:\mathrm{colour} \\ $$$$\mathrm{respectively}.\:\mathrm{If}\:\mathrm{they}\:\mathrm{are}\:\mathrm{thrown}\:\mathrm{up}\: \\ $$$$\boldsymbol{\mathrm{thrice}}\:\mathrm{in}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{competition}\:\mathrm{and}\:\mathrm{a} \\ $$$$\mathrm{contestant}\:\mathrm{picks}\:\mathrm{one}\:\mathrm{at}\:\mathrm{random}\:\mathrm{on} \\ $$$$\mathrm{each}\:\mathrm{throw},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{he}\:\mathrm{picks}\:\mathrm{a}_{} \\ $$$$\:\:\left({a}\right)\:\mathrm{different}\:\mathrm{shape}\:\mathrm{on}\:\mathrm{each}\:\mathrm{throw}?_{} \\ $$$$\:\:\left({b}\right)\:\mathrm{triangular}\:\mathrm{piece}\:\mathrm{which}\:\mathrm{is}\:\mathrm{red}\:\mathrm{in} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{colour}\:\mathrm{on}\:\mathrm{the}\:\mathrm{second}\:\mathrm{throw}?_{} \\ $$$$\:\:\left({c}\right)\:\mathrm{blue}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{confetti}\:\mathrm{at}\:\mathrm{least} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{twice}? \\ $$

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