In a game, one player throws two fair, six-sided die at the same time.
In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a one or five on either die, that player wins. What is the probability that a player wins after playing the game once?
Answer/Solution
5/9
Steps/Work
We're looking for the number of outcomes that include AT LEAST a 1 or a 5.
#getting a one in 1st die = {(1,1), (1,2), ...(1,6) }= 6
#getting a one in 2nd die {(2,1), (3,1), ...(6,1) } = 4 [exclude 1,1 and 5,1] since it will be counted twice
#getting a five in 1st die {(5,1), (5,2), ...(5,6) }= 6
#getting a five in 1st die {(2,5), (3,5), ...(6,5) } = 4 [exclude 1,5 and 5,5] since it will be counted twice
Total possibilities = 20
Probability of rolling at least a 1 or a 5 on two dice: 20/36 = 5/9
E
#getting a one in 1st die = {(1,1), (1,2), ...(1,6) }= 6
#getting a one in 2nd die {(2,1), (3,1), ...(6,1) } = 4 [exclude 1,1 and 5,1] since it will be counted twice
#getting a five in 1st die {(5,1), (5,2), ...(5,6) }= 6
#getting a five in 1st die {(2,5), (3,5), ...(6,5) } = 4 [exclude 1,5 and 5,5] since it will be counted twice
Total possibilities = 20
Probability of rolling at least a 1 or a 5 on two dice: 20/36 = 5/9
E