Question

Solve problems involving compound events and write about the solutions.
You are playing a game with your friends, Alex and Jeff. The first player who rolls a total of seven using two number cubes gets to start the game. Explain how to find the probability that you will roll a total of seven on your first try.

Answer 1

First find the chance a single roll of two number cubes totals 7. There are 6 favorable outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 possible, so
P(7 on one roll) = 6/36 = 1/6,
and P(not 7) = 5/6.

Assuming players roll in order Alex, Jeff, then you, for you to roll a 7 on your first try both Alex and Jeff must fail and then you must succeed. Those are independent events, so
P = P(Alex fails) · P(Jeff fails) · P(you succeed)
= (5/6) · (5/6) · (1/6)
= 25/216 ≈ 0.1157 (about 11.57%).

(If instead you roll first, your probability of a 7 on your first try is simply 1/6.)