Q:

Jeff can win the game if he rolls 11 on the two number cubes. If he rolls an even sum, however, he will lose his next turnWhat is the probability that he will win the game? What is the probability that he will lose his next turn?

Accepted Solution

A:
Answer:What is the probability that he will win the game?  1/18What is the probability that he will lose his next turn? 1/2Step-by-step explanation:All explanations here suppose the cubes are regular 6-facets cubes numbered 1 to 6.  There are many different types of number cubes, and the question doesn't specify a type used.What is the probability that he will win the game?Out of the 36 possible combinations for 2 cubes to produce numbers, only 2 will give a 11.  If the first cube gives a 6 and the second cube a 5, or vice-versa.So, out of the 36 possible outcomes, only 2 are good... so 2/36 or 1/18.What is the probability that he will lose his next turn? For each time the first cube lands on 1, there are 3 possibilities that the number shown on the second cube  (if that second cube shows 1, 3 or 5) will make an even total.  That is true for each of the six possible values of the first cube.So, in total, there are 18 possibilities out of 36 to throw an even sum, so 18/36 or 1/2.