Bag A contains 3 red and 5 white balls and bag B contains 4 red and 4 white balls. A bag is selected at random, and a ball is drawn. Then the probability of getting a red ball is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → more than 0.33 but less than 0.50
By the theorem of total probability, with each bag chosen with probability \( \frac{1}{2} \):
\( \displaystyle P(\text{Red})=\frac{1}{2}\cdot\frac{3}{8}+\frac{1}{2}\cdot\frac{4}{8} \)
\( \displaystyle =\frac{3}{16}+\frac{4}{16} \)
\( \displaystyle =\frac{7}{16} \)
\( \displaystyle \frac{7}{16}=0.4375 \)
Since 0.33 < 0.4375 < 0.50, the probability is more than 0.33 but less than 0.50.
Shortcut: The total probability is an average of \( \frac{3}{8}=0.375 \) and \( \frac{4}{8}=0.5 \), so it must lie between 0.375 and 0.5; only Option (2) contains this range.