Question

Fifty tickets numbered with consecutive integers are in a jar. Two are drawn at random and without replacement. What is the probability that the absolute difference between the two numbers is 10 or less? Express your answer as a common fraction.

a) 19/25
b) 9/25
c) 1/10
d) 7/25

Answer 1

The probability that the absolute difference between the two numbers is 10 or less is 19/25.

Step-by-step explanation:

To find the probability that the absolute difference between the two numbers is 10 or less, we need to consider the possible pairs of numbers that satisfy this condition.

There are 10 pairs of consecutive integers that have an absolute difference of exactly 10: (1, 11), (2, 12), ..., (10, 20).

There are also 9 pairs of consecutive integers that have an absolute difference of exactly 9: (2, 11), (3, 12), ..., (9, 18).

Therefore, the total number of pairs of numbers that satisfy the condition is 10 + 9 = 19. Since there are a total of (50 choose 2) = 1225 possible pairs, the probability is 19/1225, which simplifies to 19/25.