Question

Two dice are thrown at the same time find the probability of getting different numbers on both dice

Answer 1

$\mathrm{SOLUTION}$

$\bold{Given:}$ Two dice are thrown at same time

$\bold{To\:Find:}$ Probability of getting different numbers on both the dice

$\underline{Here\:it\:goes}$

>>>Since there are two dice , therefore total number of outcomes = (6×6) = 36

Now let us note down different outcomes-

(1, 2) (2, 1) (3, 1) (4, 1) (5, 1) (6 ,1)

(1, 3) (2, 3) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 4) (2, 4) (3, 4) (4, 3) (5, 3) (6, 3)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 4) (6, 4)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 5)

Favourable Outcomes = 30

Therefore ,

Probability = $\dfrac{Favourable\:Outcomes}{Total\:Outcomes}$

Hence, Probability = $\dfrac{30}{36}$

$\huge\mathrm{Final\:Answer:}$ $\dfrac{5}{6}$

Answer 2

$\huge{\underline{\sf{Answer-}}}$

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$\sf{\underline{Probability\:of\:getting\:different\:number\:is\:\dfrac{5}{6}}}$

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$\huge{\underline{\sf{Explanation-}}}$

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$\begin{lgathered}\bold{Given} \begin{cases}\sf{Two\:dice\:are\:thrown\:at\:same\:time.} \\ \sf{Probability\:of\:getting\:different\:number\:on\:both\:dice\:=\:?}\end{cases}\end{lgathered}$

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Total outcomes : 36

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(1,1)⠀⠀(1,2)⠀⠀(1,3)⠀⠀(1,4)⠀⠀(1,5)⠀⠀(1,6)

(2,1)⠀⠀(2,2)⠀⠀(2,3)⠀⠀(2,4)⠀⠀(2,5)⠀⠀(2,6)

(3,1)⠀⠀(3,2)⠀⠀(3,3)⠀⠀(3,4)⠀⠀(3,5)⠀⠀(3,6)

(4,1)⠀⠀(4,2)⠀⠀(4,3)⠀⠀(4,4)⠀⠀(4,5)⠀⠀(4,6)

(5,1)⠀⠀(5,2)⠀⠀(5,3)⠀⠀(5,4)⠀⠀(5,5)⠀⠀(5,6)

(6,1)⠀⠀(6,2)⠀⠀(6,3)⠀⠀(6,4)⠀⠀(6,5)⠀⠀(6,6)

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Favourable Outcomes = 30

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$\large{\boxed{\red{\sf{Probability_(e)\:=\:\dfrac{Favourable\:Outcomes}{Total\:Outcomes}}}}}$

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$\small{\sf{Putting\:the\:values-}}$

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: $\implies$ $\sf{Probability\:={\cancel{\dfrac{30}{36}}}}$

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: $\implies$ $\sf{Probability\:=\:\dfrac{5}{6}}$

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$\therefore$ $\sf{\underline{Probability\:of\:getting\:different\:number\:is\:\dfrac{5}{6}}}$