# Thread: Coins and Dice Probabaility

1. ## Coins and Dice Probabaility

You have a fair coin. Your friend has a fair die you flip your coin 10 times. Your friend rolls his die 15 times. What is the probability that you get "heads" exactly the same number of times your friend gets "3" or "5". Leave your answer in the form of a summation. No need to simplify! Assume independence here.

10Cn (1/2)^n (1/2)^10-n (coin)
15Cn (1/3)^n (2/3)^15-n (dice)

Sum (n = 1 to 10) of
10Cn (1/2)^n (1/2)^10-n * 15Cn (1/3)^n (2/3)^15-n

Can someone confirm this?

2. It looks right, except that you left out the ZERO
Both of you might get zero heads...

3. Originally Posted by matheagle
It looks right, except that you left out the ZERO
Both of you might get zero heads...
So in this problem, you also need to include the zero heads?

4. You are summing over the possibilities of 1 through 10 successes
A success is when we have the same number of heads and having a 3 or 5 on the die.
So why can't they have zero successes?