A bag contains 4 red and 6 green balls. A ball is drawn at random, its colour is noted and is returned to the bag. One additional ball of the colour drawn is put in the bag. Again a ball is then drawn from the bag. The probability of this ball to be of green colour is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{3}{5}\)
The second draw depends on the colour of the first, so use the theorem of total probability.
If the first ball is green (probability \(\frac{6}{10}\)), the bag then has 4 red and 7 green balls. If it is red (probability \(\frac{4}{10}\)), the bag has 5 red and 6 green balls. In both cases there are 11 balls.
\( \displaystyle P(\text{second green}) = \frac{6}{10}\cdot\frac{7}{11} + \frac{4}{10}\cdot\frac{6}{11} \)
\( \displaystyle P(\text{second green}) = \frac{42 + 24}{110} = \frac{66}{110} = \frac{3}{5} \)
Tip: When the drawn ball is returned together with one more ball of the same colour, the chance of green on the second draw equals the chance on the first draw, here \(\frac{6}{10} = \frac{3}{5}\).