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