1. Tardigrade
  2. Question
  3. Mathematics
  4. A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement. The probability that exactly two of the three balls were red, the first ball being red, is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A bag contains $5$ red and $3$ blue balls. If $3$ balls are drawn at random without replacement. The probability that exactly two of the three balls were red, the first ball being red, is

Probability - Part 2

Solution:

Since, the first ball drawn is red so, we are left with $4$ red and $3$ blue balls. Now, we draw two balls out of which one should be red and other should be blue.
$\therefore $ Required probability $= P\left\{\left(RB\right), \left(BR\right)\right\}$
$= P \left(RB\right) + P\left(BR\right)$
$= \frac{4}{7}\cdot\frac{3}{6}+\frac{3}{7}\cdot\frac{4}{6}$
$= 2\times\frac{2}{7} = \frac{4}{7}$