Question

A bag contains 5 red balls and some blue balls. If the probability of drawing a
blue ball is double that of a red ball, determine the number of blue balls in a bag....


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Answer 1

$\tt\it\bf\it\bm{\mathcal{\fcolorbox{blue}{white}{\red{Question:-}}}}$

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A bag contains 5 red balls and some blue balls. If the probability of drawing a

A bag contains 5 red balls and some blue balls. If the probability of drawing ablue ball is double that of a red ball

$\tt{\red{</strong><strong>we\</strong><strong>:</strong><strong>have\</strong><strong>:</strong><strong>to\</strong><strong>:</strong><strong> determine</strong><strong>\</strong><strong>:</strong><strong>the\</strong><strong>:</strong><strong> number</strong><strong>}}$

$\tt{\red{</strong><strong>of\:blue\:balls\:!!</strong><strong> </strong><strong> </strong><strong>}}$

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$\tt\it\bf\it\bm{\mathcal{\fcolorbox{blue}{white}{\red{Solution:-}}}}$

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Let, the number of blue ball be x

Number of red ball = 5

Total number of balls = 5+x

P($\tt{\red{red ball}}$)=

$\frac{5}{(x + 5)}$

P($\tt{\blue{blue ball}}$)=

$\frac{x}{(x + 5)}$

$\tt\it\bf\it\bm{\mathcal{\fcolorbox{blue}{white}{\red{Given:-}}}}$

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P($\tt{\blue{blue ball}}$)= 2*P($\tt{\red{red ball}}$)

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$= > 2( \frac{5}{x + 5} ) = \frac{x}{x + 5}$

$= > 10(x + 5) = {x}^{2} + 5x$

$= > {x}^{2} - 5x - 50 = 0$

$= > {x}^{2} - 10x + 5x - 50 = 0$

$= > x(x - 10) + 5(x - 10) = 0$

$= > (x - 10)(x + 5) = 0$

$= > now \: either \: (x - 10) = 0 \\ \: \: \: \: \: \: \: \: or \: (x + 5) = 0$

$x = 10 \: or \: - 5$

But, number of ball cannot be negative.

hence, the number of blue ball is 10

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Answer 2

Given:

Number of Red balls = 5

P(drawing a blue ball) = 2{ P (drawing a red ball) }

To find:

The number of blue balls in the bag

Answer:

Now,

Let the number of blue balls be x

The total number of balls in the bag = ( 5+x )

And the probability of

▪︎drawing a red ball = 5 / (5+x)

▪︎drawing a blue ball = x / (5+x)

So,

x / (5+x) = 2[ 5 / (5+x) ] {Given}

= x / 5+x = 10 / 5+x (5+x will cancel out)

=> x = 10

Hence, The number of of blue balls in the bag is 10.

Total number of balls are 15 . (5+x)

P(red balls) = 5/ 15

= 1/3

P(blue balls) = 10/ 15

Please mark brainliest.