Question

Suppose, R is a random real number between 5 and 9. What is the probability R is closer to 5 than it is to 6?

(a) 12.5%

(b) 18%

(c) 73%

(d) 39.8%

This question was addressed to me in quiz.

My question is from Geometric Probability topic in portion Discrete Probability of Discrete Mathematics

Answer 1

Correct answer is (a) 12.5%

The best I can explain: Since there are infinitely many possible outcomes for the value of X we will take the equally likely outcomes as random points along the number line from 5 to 9. R will be closer to 5 than it is to 6 if R<5.5. We can easily see it by drawing a probability line. Here, P(R is closer to 5 than to 6) = (length of segment where 5<R<5.5)/(length of segment where (5<R<9) = 0.5/4 = 0.125 = 12.5%.