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EEJ MAIN Mathematics QUESTION #6981
Question 1

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.

  • $\dfrac{1}{5}$
  • $\dfrac{3}{4}$
  • $\dfrac{3}{10}$
  • $\dfrac{2}{5}$✔️
Correct Answer Explanation

Initially: 4 red, 6 black (10 total).

Case 1 — 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 — 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: $\dfrac{4}{10}\cdot\dfrac{1}{2}+\dfrac{6}{10}\cdot\dfrac{1}{3} = \dfrac{2}{10}+\dfrac{2}{10} = \dfrac{4}{10} = \dfrac{2}{5}$