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Question

In an urn, there are 30 blue balls, 20 red balls and x green balls and y black balls. A ball is taken at random from the urn. The probability that the chosen ball is not red in colour is 34 and it is known that the number of black balls is twice the number of green balls. Find the value of y-x.

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Solution

Number of blue balls = 30

Number of red balls = 20

Number of green balls = x

Number of black balls = y

Total number of balls = 30+ 20 + x + y = 50 + x + y

14=2050+x+y

Subtract 34 from both sides and rearrange,

14=2050+x+y

Cross multiplying

50 + x + y = 80

Or, x + y = 30 ...........(i)

It is given that the number of black balls (y) is twice as many as green balls (x)

i.e y = 2x ...........(ii)

Substituting (ii) in Equation (i)

we have x + 2x = 30

3x = 30

x = 10

From (ii)

we have x + 2x = 30

3x = 30

x = 10

From (ii)

y = 2( 10) = 20

∴ y–x=20−10=10

∴ y–x=20−10=10

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