Question

A bag contains 5 black, 7 red and 3 white balls. One ball is drawn at random. Find the probability of drawing the ball is (i) red (ii) black (iii) not black.

Hint:

Always compute total outcomes first. Then probability = $\dfrac{\text{favourable outcomes}}{\text{total outcomes}}$. Use $P(\text{not A})=1-P(\text{A})$ for quicker calculation.

Answer 1

Total balls $=5+7+3=15$. (i) Probability of red: \[ P(\text{red})=\frac{7}{15} \] (ii) Probability of black: \[ P(\text{black})=\frac{5}{15}=\frac{1}{3} \] (iii) Probability of not black: \[ P(\text{not black})=1-P(\text{black})=1-\frac{5}{15}=\frac{10}{15}=\frac{2}{3} \] \[ \boxed{P(\text{red})=\tfrac{7}{15}, P(\text{black})=\tfrac{1}{3}, P(\text{not black})=\tfrac{2}{3}} \]