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

[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.