Question

roll and win
you begin the game roll and win by picking a number. then you roll two regular dice, each numbered 1 through 6, and add the numbers that come up together. if the sum is the number you chose, you win a point. for example, if you choose \11\, and a 6 and a 5 are rolled, you win!
a. what is the sample space, which can be thought of as the set of all the possible outcomes, when two dice are rolled and their numbers added?
hint (a):
what sums can occur when two dice are rolled?
b. one way to analyze this situation is to make a table of all the possible outcomes like the one below. copy and complete this table of sums on your paper. are each of the outcomes in this table equally likely?

Explanation:

Step1: Determine the minimum and maximum sum

When rolling two dice, the minimum sum occurs when both dice show \(1\) (i.e., \(1 + 1=2\)). The maximum sum occurs when both dice show \(6\) (i.e., \(6+6 = 12\)).

Step2: List all possible sums

The possible sums range from \(2\) to \(12\). So the sample space \(S=\{2,3,4,5,6,7,8,9,10,11,12\}\)

Answer:

The sample space is \(S = \{2,3,4,5,6,7,8,9,10,11,12\}\)