Question

. A box contains 15 red balls, 18 white balls. One ball is taken out of the box at random. What is the probability that the ball taken out will be not red.​

Answer 1

GIVEN :–

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• A box contains 15 red balls, 18 white balls.

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• One ball is taken out of the box at random.

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TO FIND :–

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• Probability that the ball taken out will be not red = ?

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SOLUTION :–

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• We know that –

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☆ Probability = n(E)/n(S)

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▪︎ E → Taken ball is not red.

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=> E → Taken ball is white.

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=> n(E) = $\bf ^{18} c_{1}$

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▪︎ S → One ball take from 33 balls.

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=> n(S) = $\bf ^{33} c_{1}$

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• So that –

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$\bf \implies \:Probability = \dfrac{^{18} c_{1}}{^{33} c_{1}}$

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• Using identity –

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$\bf \implies ^{n} c_{r} = \dfrac{n!}{(n - r)!(r)!}$

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• So that –

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$\bf \implies \:Probability = \dfrac{ \dfrac{18!}{(18 - 1)!(1)!}}{\dfrac{33!}{(33 - 1)!(1)!}}$

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$\bf \implies \:Probability = \dfrac{ \dfrac{18!}{(17)!}}{\dfrac{33!}{(32)!}}$

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$\bf \implies \:Probability = \dfrac{ \dfrac{(18)(17)!}{(17)!}}{\dfrac{(33)(32!)}{(32)!}}$

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$\bf \implies \large{ \boxed{ \bf Probability = \dfrac{18}{33}}}$

Answer 2

$\red{GIVEN :–}$

• A box contains 15 red balls, 18 white balls.

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• One ball is taken out of the box at random.

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$\red{To \ FIND :–}$

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• Probability that the ball taken out will be not red = ?

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$\huge\pink{\underline{\underline{\bf{\blue{SOLUTION :–}}}}}$

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$\red{ \ We \ know \ that –}$

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★ Probability = n(E)/n(S)

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▪︎ E → Taken ball is not red.

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=> E → Taken ball is white.

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=>{n(E) = $\bf ^{18} c_{1}$

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▪︎ S → One ball take from 33 balls.

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=> n(S) = $\bf ^{33} c_{1}$

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$\red{So \ that –}$

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$\bf \implies \:Probability = \dfrac{^{18} c_{1}}{^{33} c_{1}}$

$\red{Using \ identity –}$

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$\bf \implies ^{n} c_{r} = \dfrac{n!}{(n - r)!(r)!}$

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$\red{So \ that –}$

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$\bf \implies \:Probability = \dfrac{ \dfrac{18!}{(18 - 1)!(1)!}}{\dfrac{33!}{(33 - 1)!(1)!}}$

$\bf \implies \:Probability = \dfrac{ \dfrac{18!}{(17)!}}{\dfrac{33!}{(32)!}}$

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$\bf \implies \:Probability = \dfrac{ \dfrac{(18)(17)!}{(17)!}}{\dfrac{(33)(32!)}{(32)!}}$

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$\bf \implies \large{ \boxed{ \bf Probability = \dfrac{18}{33}}}$