Answer: 5/48
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Step-by-step explanation:
Grab some graph paper, or open up a spreadsheet.
Make a table that has 4 rows and 5 columns as indicated in figure 1. This section will focus on that figure only.
The left edge is marked with A through D from the spinner on the left. The corresponding probabilities in red are 1/4, 1/2, 1/8, 1/8
The top side is marked with A through E. Those probabilities in red are 1/6, 1/6, 1/6, 1/3, 1/6
Each fraction inside the table is a result of multiplying the outer red fractions.
For instance, we have 1/24 in the upper left corner because (1/4)*(1/6) = 1/24.
I have highlighted in yellow the cells that correspond to getting A and D in either order. We then add up the fractions inside those yellow cells.
1/12 + 1/48 = 4/48 + 1/48
= (4+1)/48
= 5/48 is the final answer.
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The previous section used figure 1.
This current section will use figure 2. Ignore this current section if you prefer figure 1 better.
For figure 2, we have a table that has 8 rows and 6 columns. Pay close attention that some of the letters A through E repeat themselves.
For example, the letter "A" repeats itself on the left spinner. We have two copies of "A" out of 8 rows total. So the chances of landing on "A" are 2/8 = 1/4.
In figure 2, I have marked the cells that correspond to getting A and D in either order. These are marked in green. There are 5 such cells.
This is out of the 8*6 = 48 cells total.
That's another way to arrive at 5/48