In order to win a game, a player must throw two fair dice and the sum...

In order to win a game, a player must throw two fair dice and the sum of the dice needs to be either 4 or less or 10 or more for the player to win.

What is the probability that the sum of the dice is 4 or less?

What is the probability that the sum of the dice is 10 or more?

What is the probability that the player will win the game?

Solutions

Expert Solution

When two dice are thrown, Number of possible outcomes = 6 x 6 = 36

Following are the cases where ,

the sum is equal to 2 : (1,1)

the sum is equal to 3 : (1,2) (2,1)

the sum is equal to 4 : (1,3) (2,2) (3,1)

Number of outcomes where the sum is 4 or less = 1+2+3 = 5

Probability that the sum of the dice is 4 or less = Number of outcomes where the total is either 4 or less / Total number of outcomes = 5/36

Probability that the sum of the dice is 4 or less = 5/36

Following are the cases where ,

the sum is equal to 10 : (4,6) (5,5) (6,4)

the sum is equal to 11 : (5,6) (6,5)

the sum is equal to 12 : (6,6)

Number of outcomes where the sum is 10 or more = 1+2+3 = 5

probability that the sum of the dice is 10 or more = Number of outcomes where the total is 10 or more / Total number of outcomes = 5/36

Probability that the sum of the dice is 10 or more = 5/36

The sum of the dice needs to be either 4 or less or 10 or more for the player to win.

Probability that the player will win the game = Probability that the sum of the dice (4 or less) or (10 or more) = Probability that the sum of the dice is 4 or less + Probability that the sum of the dice is 10 or more = 5/36 + 5/36 = 10/36 = 5/18

orchestra answered 9 months ago

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