A bag contains x red, 2x−32x-3 blue and 2x+32x+3 green balls. If two balls are randomly drawn from the bag, the probability that a red ball and a green ball are drawn is 1/5. What is the probability of drawing a blue ball from the bag
Answers
Given : A bag contains x red, 2x−32x-3 blue and 2x+32x+3 green balls. If two balls are randomly drawn from the bag, the probability that a red ball and a green ball are drawn is 1/5.
To find : probability of drawing a blue ball from the bag
Solution:
Red Balls = x
Blue Balls = 2x - 3
Green Balls = 2x + 3
Total Balls = x + 2x-3 + 2x + 3 = 5x
probability that a red ball and a green ball are drawn
Red green + green Red
= (x/5x)((2x + 3)/(5x - 1)) + ((2x + 3)/5x)(x/(5x - 1))
= 2x(2x + 3)/(5x(5x - 1))
or ˣC₁* ²ˣ⁺³C₁ / ⁵ˣC₂ = 2x(2x + 3)/ (5x(5x - 1))
2x(2x + 3)/5x(5x - 1) = 1/5
= 4x² + 6x = 5x² - x
=> x² = 7x
=> x = 7
Red Balls = 7
Blue Balls = 11
Green Balls = 17
Total Balls = 35
probability of drawing a blue ball from the bag = 11/35
11/35 is the probability of drawing a blue ball from the bag
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