Question

A point (𝑎, 𝑏) is chosen at random from the rectangular region [0, 2]×[0, 4]. Then, the probability that the area of the region
𝑅={(𝑥, 𝑦) ∈ ℝ × ℝ ∶ 𝑏𝑥 + 𝑎𝑦 ≤ 𝑎𝑏, 𝑥, 𝑦 ≥ 0}
will be less than 2, equals

• A. $\frac{1+In\,2}{4}$
• B. $\frac{1+In\,2}{2}$
• C. $\frac{2+In\,2}{4}$
• D. $\frac{1+2\, +In\,2}{4}$

Answer 1

Answer: (B)

$\frac{1+In\,2}{2}$

Answer 2

The correct option is (B): $\frac{1+In\,2}{2}$