Two fair dice are rolled. Let [math]X[/math] be the absolute value of the difference between the two numbers on the dice. Calculate the probability that [math]X\lt 3 [/math].

• 2/9
• 1/3
• 4/9
• 5/9
• 2/3

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

The dice rolls that satisfy this event are (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (3,5), (4,2), (4,3), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,4), (6,5), and (6,6). They represent 24 of the 36 equally likely outcomes for a probability of 2/3.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.