Question
In a box, there are three different colour cubes: blue,
green, and orange. The sum of the number of green and blue cubes in the box equals the number of orange cubes. The probability of picking two blue cubes from the box is (1/22). If the total number of blue, green, and orange cubes in the box is 24, then find out the number of green cubes in the box.Solution
ATQ, Let's denote the number of blue, green, and orange cubes as ‘B’, ‘G’, and ‘O’ respectively. Given: G+B = O and B+G+O = 24. Probability of picking two blue cubes = (1/22) implies [B(B-1)]/(24x23) = 1/22. Simplifying: B(B-1) = 24. Solving the quadratic equation B²-B-24=0 gives B = 6 or B = -4 (discard the negative value). With B = 6, substitute back to find O = 24 - B - G = 24 - 6 - G = 18 - G. Since G+B = O, we get G + 6 = 18, thus G = 12. Number of green cubes = 12.
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