A box contains black, white and red identical balls. The probability of picking a black ball at random from the box is \(\frac{3}{10}\) and the probability of picking a white ball at random is \(\frac{2}{5}\). If there are 30 balls in the box, how many of them are red?
Total no of balls = 30
Let x = no. of red balls
Pr(red) = \(\frac{x}{30}\)
Pr(black) = \(\frac{3}{10} = \frac{9}{30}\)
Pr(white) = \(\frac{2}{5} = \frac{12}{30}\)
No. of black balls = 9
No. of white balls = 12
9 = 12 + x = 30
x = 30 - 21
x = 9
No. of red balls = 9
OR
Let w = no of white balls
B = no of black balls
R = no of red balls
Pr(black balls) = \(\frac{3}{10}\)
Pr(white balls) = \(\frac{2}{5}\)
But Pr(white balls) = \(\frac{2}{5}\) = \(\frac{W}{30}\)
cross multiply
W = no of white balls = 12
Pr(black balls) = \(\frac{3}{10}\) = \(\frac{B}{30}\)
cross multiply
B = no of black balls = 9
Total number of balls in the basket = W + B + R = 30 ( given)
= 12 + 9 + R = 30
R = 30 - 12 - 9 = 9
Therefore, the no of red balls = 9.
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