Study questions platform-wide or filter by specific tests with correct answers revealed.
A bag has 4 red and 6 black balls. One ball is drawn, observed, and returned along with 2 more balls of the same colour. A second ball is then drawn. Find the probability that the second ball drawn is red.
Initially: 4 red, 6 black (10 total).
Case 1 โ First ball is red (prob $= \frac{4}{10}$):
Bag becomes: 6 red, 6 black (12 total). $P(\text{red 2nd}) = \frac{6}{12} = \frac{1}{2}$.
Case 2 โ First ball is black (prob $= \frac{6}{10}$):
Bag becomes: 4 red, 8 black (12 total). $P(\text{red 2nd}) = \frac{4}{12} = \frac{1}{3}$.
Total: $\dfrac{4}{10}\cdot\dfrac{1}{2}+\dfrac{6}{10}\cdot\dfrac{1}{3} = \dfrac{2}{10}+\dfrac{2}{10} = \dfrac{4}{10} = \dfrac{2}{5}$
Sign in to join the conversation and share your thoughts.
Log In to Comment