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A box contains red, green, and blue colored balls, such that the probability of picking a blue ball is 37.5% of the probability of picking a red ball, and the probability of picking a red ball is 88.89% of the probability of picking a green ball. If the box contains 8 red balls, then how many total balls are there in the box?

A box contains red, green, and blue colored balls, such that the probability of picking a blue ball is 37.5% of the probability of picking a red ball, and the probability of picking a red ball is 88.89% of the probability of picking a green ball. If the box contains 8 red balls, then how many total balls are there in the box? Correct Answer 20

Given,

P(blue) = 37.5% of P(red)

⇒ P(blue) = 3/8 × P(red)      ----(1)

Also,

P(red) = 88.89% of P(green)

⇒ P(red) = 8/9 × P(green)

⇒ P(green) = 9/8 × P(red)        ----(2)

∵ P(red) + P(green) + P(blue) = 1

Upon substituting from (1) and (2), we get,

⇒ P(red) + 9/8 × P(red) + 3/8 × P(red) = 1

⇒ 5/2 × P(red) = 1

⇒ P(red) = 2/5

∵ P(red) = No. of red balls/Total no. of balls

⇒ 2/5 = 8/Total no. of balls

⇒ Total no. of balls = 8 × 5/2

∴ Total no. of balls in box = 20

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