Question

You spin two spinners, each of which is divided into five congruent sections numbered 1 to 5. List all possible outcomes. Then find the probability of getting the same number on both spins. Show your work.

Answer 1

please help!

Answer 2

each spinner has 5 possible outcomes
by the counting principle the combined number of outcomes is \(5\times 5=25\)

Answer 3

we can write them as ordered pairs, for example
(1,1) (1,2) (1,3) (1,4) (1,5)
(2,1) (2,2) (2,3) (2,4) (2,5)

and so one
there will be 25 of them

Answer 4

since they are all equally likely, the probability of any one outcome is \(\frac{1}{25}\)
to find the probability that the numbers are both the same, count the possibilities, put that number over 25

Answer 5

The sample space has 25 possible combinations of numbers. These can be set out in column form as follows:
5,5 4,5 3,5 2,5 1,5
5,4 4,4 3,4 2,4 1,4
5,3 4,3 3,3 2,3 1,3
5,2 4,2 3,2 2,2 1,2
5,1 4,1 3,1 2,1 1,1