Question

Jessica is playing a game with the two spinners shown below: She will win the game if the product of the two spinners is an even number greater then 12. What are all the possible outcomes in which Jessica wins the game?

Answer 1

So basically we need to find all the products between one number from one spinner and another from the other spinner that are even and greater than 12. So let's begin by assuming we have a 1 in the first spinner. The four posible results given by multiplying 1 with theresult of the second spinner are:

`\begin{gathered} 1\cdot2=2 \\ 1\cdot4=4 \\ 1\cdot6=6 \\ 1\cdot8=8 \end{gathered}`

None of them is greater than 12 so we can discard all. We can do the same calculations but assuming that the result of the first spinner was 2:

`\begin{gathered} 2\cdot2=4 \\ 2\cdot4=8 \\ 2\cdot6=12 \\ 2\cdot8=16 \end{gathered}`

The only result that is greater than 12 and even is 16 so we add it to our list of winning outcomes.

Now we do the same assuming the result of the first spinner was 3:

`\begin{gathered} 3\cdot2=6 \\ 3\cdot4=12 \\ 3\cdot6=18 \\ 3\cdot4=24 \end{gathered}`

We have two results greater than 12 and even: 18 and 24. So for now our winning outcomes are {16,18,24}. Let's see what happens when the result of the first spinner is 4:

`\begin{gathered} 4\cdot2=8 \\ 4\cdot4=16 \\ 4\cdot6=24 \\ 4\cdot8=32 \end{gathered}`

So we have three results greater than 12 and even but we already have two of them: 16 and 24. Then we just need to add 32 to our list. Then the set of outcomes in which Jessica wins is:

`\mleft\lbrace16,18,24,32\mright\rbrace`

Then the answer is the fourth option.