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 heads.

Explanation:

Step1: Recall the formula for the expected value of a binomial distribution

The formula for the expected value \(E(X)\) of a binomial distribution \(X\sim B(n,p)\) is \(E(X)=np\). Here, \(n = 10\) (number of coin - flips) and \(p=\frac{1}{2}\) (probability of getting a head in a single flip of a fair coin).

Step2: Calculate the expected value

Substitute \(n = 10\) and \(p=\frac{1}{2}\) into the formula \(E(X)=np\). So, \(E(X)=10\times\frac{1}{2}\).

Answer:

\(5\)