### Instruction: What is the probability that Fatima gets fewer heads than tails if she flips 10 coins?### Response: To answer this question, I need to find the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes is 2^10, since each coin has two choices and they are independent.
The number of favorable outcomes is the sum of the number of ways to get k heads and 10-k tails for k = 0, 1, 2, ..., 4.
To find the number of ways to get k heads and 10-k tails, I can use the binomial coefficient (10 choose k), which is equal to 10!/(k!(10-k)!).
So the number of favorable outcomes is (10 choose 0) + (10 choose 1) + (10 choose 2) + (10 choose 3) + (10 choose 4).
I can use a calculator or the Pascal's triangle to find these values.
They are 1 + 10 + 45 + 120 + 210 = 386.
So the probability of getting fewer heads than tails is 386/2^10, which simplifies to 193/512.