SOLUTION: A pair of dice is rolled. Find the probabilities of the given events.
a. The sum of four.
b. The sum of four, given that the sum is odd.
c. The roll is doubles, given that the
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Question 322673: A pair of dice is rolled. Find the probabilities of the given events.
a. The sum of four.
b. The sum of four, given that the sum is odd.
c. The roll is doubles, given that the sum is four.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability of anything is the number of ways that it can happen that you would consider a success divided by the number of ways it can happen total -- successes and failures.
There are 36 possible outcomes for rolling a standard pair of 6-sided dice. Dice with different numbers of sides and with different numbering than the standard 1 through 6 have different numbers of outcomes.
There are three ways to make a 4. 1,3 2,2 and 3,1. Hence, the probability of a four is 
.
Since 4 is an even number there is no combination where the sum is 4 and the sum is odd simultaneously. The numerator of the fraction is zero.
There is only one way to roll a 4 with doubles...2 and 2. That's why they call it the "hard way" at the Craps table.
John
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