The set of all possible outcomes is {(1, B), (2, B), (3, B), (1, R), (2, R), (3, R)}, the Cartesian Product of the two sets {1, 2, 3} and {B, R}, representing outcomes on the spinning of each arrow.
What is the Cartesian Product of two sets?
The Cartesian Product of two sets A and B, written as A x B is the set of all ordered pairs (x, y), where x is an element of set A and y is an element of set B.
A x B = {(x, y): x ∈ A and y ∈ B}.
How do we solve the given question?
In the question, we are given two arrows that spin on two discs.
We are asked to write down all the possible outcomes when the two arrows spin.
We determine the outcomes for the spinning of each arrow as a set and then find all possible outcomes by doing the Cartesian Product of the two sets.
We assume set A to be the set of outcomes on the spinning of the first arrow (the number arrow).
∴ A = {1, 2, 3} (The three numbers on the disc: 1, 2, and 3).
We assume set B to be the set of outcomes on the spinning of the second arrow (the color arrow).
∴ B = {B, R} (The two colors on the disc: Blue and Red represent B and R).
Now, all possible outcomes in the spinning of the two arrows can be found by the Cartesian Product of A and B, that is,
A x B = {(1, B), (2, B), (3, B), (1, R), (2, R), (3, R)}.
∴ The set of all possible outcomes is {(1, B), (2, B), (3, B), (1, R), (2, R), (3, R)}, the Cartesian Product of the two sets {1, 2, 3} and {B, R}, representing outcomes on the spinning of each arrow.
Learn more about the Cartesian Product at
https://brainly.com/question/16628099
#SPJ2
