A-dice-is-cast-twice-and-the-sum-of-the-appearing-numbers-is-10-The-probability-that-the-number-5-has-appeared-at-least-once-is-

Question Number 201969 by BaliramKumar last updated on 17/Dec/23

$$\mathrm{A}\:\mathrm{dice}\:\mathrm{is}\:\mathrm{cast}\:\mathrm{twice},\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{appearing}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{10}. \\ $$$$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{number}\:\mathrm{5}\:\mathrm{has}\: \\ $$$$\mathrm{appeared}\:\mathrm{at}\:\mathrm{least}\:\mathrm{once}\:\mathrm{is}. \\ $$

Answered by Frix last updated on 17/Dec/23

$$\mathrm{3}\:\mathrm{possible}\:\mathrm{cases} \\ $$$$\mathrm{4}+\mathrm{6} \\ $$$$\mathrm{5}+\mathrm{5} \\ $$$$\mathrm{6}+\mathrm{4} \\ $$$$\Rightarrow\:{p}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$

Commented by BaliramKumar last updated on 17/Dec/23

$$\mathrm{Thanks}\:\mathrm{sir} \\ $$

Answered by mr W last updated on 18/Dec/23

$${p}=\frac{\mathrm{1}}{\mathrm{6}×\mathrm{6}}=\frac{\mathrm{1}}{\mathrm{36}} \\ $$

Commented by Frix last updated on 18/Dec/23

$$\mathrm{It}'\mathrm{s}\:\mathrm{after}\:\mathrm{the}\:\mathrm{throws}\:\mathrm{and}\:\mathrm{we}\:\mathrm{know}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{is}\:\mathrm{10}. \\ $$

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