The probability of drawing a one-rupee coin from a purse with two compartments, one of which contains 3 fifty paise coins and 2 one-rupee coins and other contains 2 fifty paise coins and 3 one-rupee coins, is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{1}{2} \)
Each compartment is chosen with probability 1/2. By the theorem of total probability:
\( \displaystyle P=\frac{1}{2}\cdot\frac{2}{5}+\frac{1}{2}\cdot\frac{3}{5} \)
\( \displaystyle =\frac{1}{5}+\frac{3}{10} \)
\( \displaystyle =\frac{1}{2} \)