Final answer:
To find the probability of getting more heads than your friend when flipping 11 fair coins and your friend flips 10 fair coins, you can use the concept of binomial probability by calculating the individual probabilities of each outcome where you get more heads than your friend.
Step-by-step explanation:
To find the probability that you get more heads than your friend when flipping 11 fair coins and your friend flips 10 fair coins, we can use the concept of binomial probability. Let X represent the number of heads you get and Y represent the number of heads your friend gets. We want to find P(X > Y).
To calculate this probability, we need to sum up the individual probabilities of getting each possible outcome where X is greater than Y. We can use the binomial probability formula for each outcome and then add them up.
The formula for the probability of getting exactly k successes in n trials with a probability p of success on each trial is:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Using this formula, we can calculate the individual probabilities and then sum them up to find the probability P(X > Y).