### Instruction: If Anna flips 8 coins, what is the probability that she gets more heads than tails?### Response: To solve this problem, I need to find the number of ways that Anna can get more heads than tails, and divide that by the total number of possible outcomes when she flips 8 coins.
The total number of possible outcomes is 2^8, since each coin can be either heads or tails independently.
That's 256.
To get more heads than tails, Anna needs to get at least 5 heads out of 8 coins.
How many ways can she do that?
One way to approach this is to use binomial coefficients, which tell me how many ways I can choose a subset of k items from a set of n items.
The formula for that is n!/(k!(n-k)!), where n! means n factorial, or the product of all positive integers up to and including n.
So, if I want to choose 5 heads from 8 coins, I can use the binomial coefficient 8!/(5!(8-5)!), which simplifies to 8*7*6/(3*2*1), which is 56.
Similarly, if I want to choose 6 heads from 8 coins, I can use the binomial coefficient 8!/(6!(8-6)!), which simplifies to 8*7/(2*1), which is 28.
And if I want to choose 7 heads from 8 coins, I can use the binomial coefficient 8!/(7!(8-7)!), which simplifies to 8/1, which is 8.
Finally, if I want to choose 8 heads from 8 coins, I can use the binomial coefficient 8!/(8!(8-8)!), which simplifies to 1/1, which is 1.
So, the total number of ways that Anna can get more heads than tails is 56 + 28 + 8 + 1, which is 93.
Therefore, the probability that she gets more heads than tails is 93/256, which is about 0.363.