Random statistics question

[galvin]

Playing the dice game Farkle where you have to roll a 1 or a 5 to "win".  So when rolling one die, you obviously have a 33% chance of rolling a 1 or a 5.  But if you have TWO dice to roll and only need a 1 or a 5 on either one of them, what are your odds now?

 

A friend is telling me it's 67% because you just add 33% to 33% but that doesn't sound right.  I countered, "what if you have 4 dice to roll a single 1 or 5, is it 132%?" to which he said it is. But that can't be right.

 

Anyway, if anyone is good with statistics (and I'm sure there are a ton of you here) and can answer this with an explanation, it would solve a heated debate amongst my friends.

 

Thanks!

[Jessica]

Well your friend is a moron. The chance of a dice roll being what you want cannot be over 100%. Come on.

 

Try looking here for some help: https://www.google.com/search?q=dice+statistics+calculator

 

 

This: http://gwydir.demon.co.uk/jo/probability/calcinfo.htm

Edited April 2, 2013 by Jessica

[Jessica]

BTW, before you explain it to your friend, make some good bets. If he thinks the odds are 132% he can't lose, right?

[galvin]

Thanks those links helped me think about it properly.  I'm fairly certain the answer is 44.4% (36 possible combinations when you roll 2 dice and 16 of them have a 1 or a 5... 16/36=44.4%)

Thanks again!

[davidannis]

For independent probabilities you just multiply 0.33 X 0.33. Think of a coin. What are the chances of 3 heads. Make a table of all outcomes (called a truth table)

 

HHH

HHT

HTH

THH

TTH

THT

HTT

TTT

 

We see one of the 8 outcomes is HHH (1/2 X 1/2 X1/2) = 1/8

 

But you don't need both outcomes to be one or five, just one, so make the truth table and count the instances of at least one one or five.

Edited April 2, 2013 by davidannis