Another Probability Problem?????

[maverick2112]

A friend challenges you to a game of "multiply the factors." Here are the rules:
GAME RULES:

Choose one player to be "odd" and the other player to be "even"
Roll a pair of 6 sided die and find the product of the two numbers
When the product is odd, the "odd" player scores a point. When the product is even the "even" player scores a point

Your friend insists that the game is fair because there are the same number of even and odds. Make a prediction - do you think the game is "fair?"

 

[Hamster]

I'll be even. There will be 27 "products" that will be even out of 36 possible combinations.

 

[maverick2112]

?????? Would'nt there be 36 probable outcomes................with 18 even products and 18 odd products????????:shrug:

 

[Blackman]

?????? Would'nt there be 36 probable outcomes................with 18 even products and 18 odd products????????:shrug:

No, because there is no side of a dice with "zero" on it.

 

[saint]

?????? Would'nt there be 36 probable outcomes................with 18 even products and 18 odd products????????:shrug:

There are 36 total possible outcomes. But 27 will be even, and 9 will be odd. This is because no matter what, the product of an even number will be even. An even x odd will give even, and even x even will give even. Only odd x odd will give odd. Look at 2 numbers to see further:

2x1=2 (e)
2x2=4 (e)
2x3=6 (e)
2x4=8 (e)
2x5=10 (e)
2x6=12 (e)

3x1=3 (o)
3x2=6 (e)
3x3=9 (o)
3x4=12 (e)
3x5=15 (o)
3x6=18 (e)

As you can see, even to odd is a 3:1 ratio, so out of 36 combos its 27even:9odd