Question

Question: What is the expected number of heads that come up when a fair coin is flipped five times?

Short answer

Answer:

The expected number of heads that come up when a fair coin is flipped five times is 2.5

Step-by-step solution

Given

A fair coin which is flipped 5 times.

To find: The expected number of heads that come up when a fair coin is flipped five times.

Formula

The expected number of successes when n mutually independent Bernoulli trials are performed, where p is the probability of success on each trial is

\(E(X) = np\)

Calculation

Here, \(n = 5\)

The coin is fair.

So, the probability to get head=\(p = \frac{1}{2}\)

The expected number of success(heads) when a fixed n mutually independent Bernoulli trials are performed, where p is the probability of success on each trial is np

\(\begin{aligned}{{}{}}{E(X) = np}\\{ = 5 \times \frac{1}{2}}\\{ = 2.5}\end{aligned}\)

Final Answer

So, the expected number of heads that come up when a fair coin is flipped five times is 2.5