In a bag, there are three different colour balls namely red, yellow and white. The sum of the number of yellow and red balls in the bag is equal to the number of white balls in the bag. The probability of picking two red balls from the bag is (3/38). If the total number of red, yellow and white balls in the bag is 20, then find out the number of yellow balls in the bag.

Solution

In a bag, there are three different colour balls namely red, yellow and white. Let’s assume the number of red, yellow and white balls in the bag is ‘R’,’Y’ and ‘W’ respectively. The sum of the number of yellow and red balls in the bag is equal to the number of white balls in the bag. Y+R = W    Eq.(i) If the total number of red, yellow and white balls in the bag is 20. R+Y+W = 20 Put Eq.(i) in the above equation. W+W = 20 2W = 20 W = 10 Put the value of ‘W’ in Eq.(i). Y+R = 10    Eq.(ii) The probability of picking two red balls from the bag is (3/38). [R(R-1)]/(20x19) = 3/38 [R(R-1)]/10 = 3/1 R(R-1) = 30 R²−R−30=0 R²−(6-5)R−30=0 R²−6R+5R−30=0 R(R-6)+5(R-6) = 0 (R-6) (R+5) = 0 So R = 6, -5 Here the value of ‘R’ cannot be negative. So R = 6 Put the vale of ‘R’ in Eq.(ii). Y+6 = 10 Y = 10-6 So the number of yellow balls in the bag = Y = 4