SOLUTION: Two standard number cubes are tossed. State whether the events are mutually exclusive by answering with yes or no. 4. The product is greater than 6; the sum is less than 7.

Question 277085: Two standard number cubes are tossed. State whether the events are mutually exclusive by answering with yes or no.
4. The product is greater than 6; the sum is less than 7.
[i think its yes]
5. The sum is odd; the product is odd.
[i think its no]

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
"Mutually exclusive" means that it is not possible for both events to occur. So if you can find even just one way for both events to occur, then the events are not mutually exclusive.

With "standard number cubes" (aka dice), the numbers that are possible on each die are 1, 2, 3, 4, 5 and 6.

4. The product is greater than 6; the sum is less than 7.
Is there a case where this is true? Answer, yes. 2*4 = 8 (which is greater than 6) and 2+4 = 6 which is less than 7. So these are not mutually exclusive events.

5. The sum is odd; the product is odd.
Let's look at how adding and multiplying work:

Numbers        Sum        Product
2 evens        Even       Even
2 odds         Even       Odd
1 even, 1 odd  Odd        Even

As you can see, the only way for two numbers to add up to an odd number is if one of them is even and one is odd. But the product of an even and an odd number is always even. So these events are mutually exclusive not matter what numbers are used (including those on dice).
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