SOLUTION: When a fair 6 sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the 5 faces that can be seen is divisible by 6?

Question 37538: When a fair 6 sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the 5 faces that can be seen
is divisible by 6?
Found 2 solutions by AnlytcPhil, fractalier:
Answer by AnlytcPhil(1806) (Show Source): You can put this solution on YOUR website!

When a fair 6 sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the 5 faces that can be seen is divisible by 6? It is absolute certain! That is, the probability is 1. Reason: Either 6 is on the bottom or it isn't 1. If 6 is not on the bottom, then 6 can be seen, and so the product will certainly be a multiple of 6, because 6 is included in the multiplying. 2. If 6 is on the bottom, then both 2 and 3 can be seen, and since their product is 6, the product of all faces that can be seen will certainly be a multiple of 6, since 2 and 3 will both be included in the multiplying. Edwin AnlytcPhil@aol.com

Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
You can either list all the six possibilities or just reason it out.
Let us do it the second way.
If the die does not have the six-pip face down, than all five of those possibilities have products divisible by six, since six is one of the faces you can see.
In the one case where the six-pip is face down, you can still see the two and the three...and of course their product is also divisible by six, so that the final answer is
100% or 1 (complete certainty)
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