Expected Heads with a Biased Coin

The count of heads is a sum of 50 indicator variables, each with the same success probability.

The mean of a Binomial$(n,p)$ random variable is $np$.

1. 1. Recognize the binomial mean

   The number of heads is Binomial$(50,0.3)$, whose mean is $np$.

2. 2. Substitute values

   Plug in $n=50$ and $p=0.3$.

   $$E[X]=50\times 0.3=15$$

Answer: 15