Q53 / 160 · AP EAMCET 2003 · Mathematics

A bag $X$ contains 2 white and 3 black balls and another bag $Y$ contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then, the probability for the ball chosen be white, is :

  • A
    $\frac{2}{15}$
  • B
    $\frac{7}{15}$
  • Correct answer
    C
    $\frac{8}{15}$
  • D
    $\frac{14}{15}$

Solution

Probability of selecting a white ball from $X$ bag $=\frac{2}{5}$ Probability of selecting a white ball from $Y$ bag $=\frac{4}{6}=\frac{2}{3}$ Probability of selecting a white ball from $X$ or $Y$ bags $=\frac{2}{5}+\frac{2}{3}=\frac{6+10}{15}=\frac{16}{15}$ Probability of selecting the white ball from one of the bags $=\frac{1}{2} \cdot \frac{16}{15}=\frac{8}{15}$

Hence, the correct answer is option: 'C'.

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