Question

Suppose a rectangle edges equals i = 4.7 and j = 8.3. Now, a straight line drawn through randomly selected two points K and L in adjacent rectangle edges. Find the condition for the probability such that the drawn triangle area is smaller than c = 9.38.

(a) K-L≤18.76

(b) K+L≤18.76

(c) KL≤18.76

(d) K/L≤18.76

The question was asked during an online interview.

Query is from Geometric Probability in chapter Discrete Probability of Discrete Mathematics

Answer 1

The correct option is (c) KL≤18.76

For explanation: The random sides of the triangle are K and L. These are the uniform random variables with uniform distributions on [0,8.3] and [0,4.7] respectively. They are independent and their joint distribution is uniform on the rectangle R = [0,8.3]∗[0,4.7]. The condition is KL/2≤9.38 ⇒ KL≤18.76. The probability that one needs is the ratio between the area under the hyperbola inside R and the area of R.