Question

I need help with the table in part B!! - Ted and his friends are playing Doubles, a game with the two spinners shown below. Each turn, a player spins both spinners. The outcome of each turn is the sum of the two numbers that the spinners land on. Extra points are scored for spinning doubles — the same number on both spinners.

Part B: Complete this table to show the sample space for each spin in the game.

Answer 1

The sample space for a particular event or number of events is simply anything that illustrates all possible outcomes of those events.
Tables can be used to display the sample space when you have two events happening, in this case, two spinners giving a number.
So, looking at the first white box (top-left corner), the number 1 that is written above it represents getting a number 1 on the spinner numbered 1 to 6 and the number of 1 written to the left of the white box represents getting a number 1 on the spinner numbered 1 to 3.
In the box, you would put 2 plus the extra points since you add the numbers on both spinners, and then add extra points because you got a double.
The numbers in each box, going along the rows (starting from top-left) are:
2 plus extra points;
3;
4;
5;
6;
7;
3;
4 plus extra points;
5;
6;
7;
8;
4;
5;
6 plus extra points;
7;
8;
9.
Notice, all possibilities of what the each of the spinners could land on and in what order are given, this is a sample space.

Answer 2

Part A.

The multiplication principle states that the total number of outcomes is found by multiplying the number of choices for each stage of the event. In this case, one spin has 6 possible outcomes and the other one has 3 possible outcomes, then, the total number of outcomes is 6*3 = 18

Part B.

The sample place is the set of all possible outcomes. With the help of the table, the outcomes are:

1 2 3 4 5 6

1 1,1 1,2 1,3 1,4 1,5 1,6

2 2,1 2,2 2,3 2,4 2,5 2,6

3 3,1 3,2 3,3 3,4 3,5 3,6