Question

Find the chance of drawing 2 white balls in succession from a bag containing 5 red and 7 white balls, the ball first drawn not being replaced.

Answer 1

Consider the given events.
A = A white ball in the first draw
B = A white ball in the second draw

\[\text{ Now }, \]
\[P\left( A \right) = \frac{7}{12}\]
\[P\left( B/A \right) = \frac{6}{11}\]
\[ \therefore \text{ Required probability } = P\left( A \cap B \right) = P\left( A \right) \times P\left( B/A \right) = \frac{7}{12} \times \frac{6}{11} = \frac{7}{22}\]