Question

Alice and Bob each choose a number uniformly (and independently) from the interval [0, 10]. What is the probability that the absolute value of the difference between their two numbers is less than 1/4

Answer 1

The probability is zero (0)

Explanation:

Given;

interval of numbers to be chosen = 0, 1, 2, 3 , 4, 5, 6, 7, 8, 9 , 10

total possible outcome = 11

The possible numbers whose absolute difference is greater than ¹/₄ includes the following;

(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,0)

The probability of this = 11 / 11 = 1

The probability that the absolute value of the difference between their two numbers is less than 1/4

`P(less \ than \ (1)/(4) ) = 1 - P(greater \ than \ (1)/(4) )\\\\P(less \ than \ (1)/(4) ) = 1 - 1 \\\\P(less \ than \ (1)/(4) ) = 0`