Question

the graph on the right shows the theoretical probability of getting a given number heads in ten flips of a fair coin. if this experiment was performed many times you would expect an average of \boxed{} heads. ten coin flips

Explanation:

Step1: Recall the concept of expected value for a binomial distribution (coin flips are a binomial experiment with \(n = 10\) trials and \(p = 0.5\) for a fair coin).

The formula for the expected value \(E(X)\) of a binomial distribution is \(E(X)=n\times p\).

Step2: Substitute the values of \(n\) and \(p\).

Here, \(n = 10\) (number of coin flips) and \(p = 0.5\) (probability of getting heads on a fair coin). So, \(E(X)=10\times0.5 = 5\).
Alternatively, from the graph (theoretical probability for ten coin flips), the distribution is symmetric around 5 (since the number of heads from 0 - 10, and the probabilities are symmetric for \(k\) and \(10 - k\) heads). The peak (or the center of symmetry) is at 5, so the expected average number of heads is 5.

Answer:

5