# Dice probability

• Nov 30th 2012, 08:17 PM
colerelm1
Dice probability
Can anyone help me get started on this problem? Any help would be appreciated:

A die has one pink side, two red sides, and three green sides.

If the die is rolled twice, what's the probability that the two shapes on top are the same?

How many times do you need to roll the die so that the probability of seeing a pink side at least twice is greater than .5? Red? Green?

Thanks
• Dec 1st 2012, 03:00 AM
Re: Dice probability
it's probability that the two shapes are red+ that they are green + that they are pink. so (1/6)²+(1/3)²+(1/2)²

you mean 0.5 ? the probability of seeing a pink side when you roll the die n times at least twice is 1-(probability of seeing 1 or 0 pink side when you roll the die n times).
probability of seeing 1 pink side when you roll the die n times is 6*(5/6)^(n-1) (Binomial Distribution, or just basic combinatorics).
probability of seeing 0 pink side when you roll the die n times is (5/6)^n (you have 5/6 chances to not have a pink side at each roll)
so you study the function to see when it becomes greater than 0.5
• Dec 2nd 2012, 08:33 AM
colerelm1
Re: Dice probability
Quote:

Originally Posted by colerelm1
How many times do you need to roll the die so that the probability of seeing a pink side at least twice is greater than .5? Red? Green?

Why wouldn't this just be:

Pink: (1/6) + (1/6) + (1/6) + (1/6) = 4/6 > 0.5 -----> 4 times
Red: (2/6) + (2/6) = 4/6 > 0.5 ------> 2 times
Green: (3/6) + (3/6) > 0.5 -----> 2 times
• Dec 2nd 2012, 08:45 AM