Question 186034
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Your number cube must have 6 faces (given that it really is a cube and not some other solid figure with a different number of faces), presumably numbered 1 through 6 like a standard die.  However, it is impossible to answer your question because you gave us no parameters regarding the spinner, such as:

Number of spaces on the spinner.

Method for numbering the spaces, i.e. all different numbers starting with 1 or some other scheme.

Write back and tell us the whole story, and someone will be able to help you.

Just as an example of the analysis that you will have to do, let's assume that your spinner has 4 spaces, numbered 1 through 4.

In that case, if the spinner lands on 1, then your possible products are 1, 2, 3, 4, 5, and 6, i.e. 1 times whatever number came up on the number cube.  If the spinner lands on 2, then your possible products are 2, 4, 6, 8, 10, and 12.  For spinner 3, you get 3, 6, 9, 12, 15, and 18.  And for spinner 4 you get 4, 8, 12, 16, 20, 24.

There are 6 times 4 = 24 different combinations of number cube and spinner, so 24 is the denominator of your probability fraction.

There is exactly 1 way to get a product of 1, so the probability of getting a 1 is *[tex \Large \frac{1}{24}].  On the other hand you have 3 different ways to get a product of 6: Spinner 1, Number Cube 6; Spinner 2, Number Cube 3; Spinner 3, Number Cube 2 -- so the probability of getting a product of 6 is *[tex \Large \frac{3}{24} = \frac {1}{8}].  You can figure out the rest of them by counting yourself and setting up the probability fraction for each possible result.

Of course, if you have a different spinner than described, you need to calculate all of the products for that different spinner.

John
*[tex \LARGE e^{i\pi} + 1 = 0]
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