A business man is expecting two telephone calls. Mr Walia may call any time between 2 p.m and 4 p.m. while Mr Sharma is equally likely to call any time between 2.30 p.m. and 3.15 p.m. The probability that Mr Walia calls before Mr Sharma is :
Step-by-Step Solution
Key Concept: Use geometric probability with 2D coordinate system where x represents Mr. Walia's call time (0 to 120 minutes after 2 PM) and y represents Mr. Sharma's call time (30 to 75 minutes after 2 PM). The favorable region is where x < y within the rectangular sample space [0,120] × [30,75].
Mr. Walia calls at $2 \text{ hrs } x \text{ minutes}$ where $x \in (0, 120)$, and Mr. Sharma calls at $2 \text{ hrs } y \text{ minutes}$ where $y \in (30, 75)$. They meet if $x < y$. Favorable region area: $\frac{1}{2}(30 + 75) \times 45 = 2362.5$. Total sample space: $45 \times 120 = 5400$. Probability: $\frac{2362.5}{5400} = \frac{7}{16}$.
Correct Answer: 4