1. **Problem statement:** Anna is a successful archer who hits the bullseye (score "10") with a probability of 75% on each shot independently. She will shoot 72 arrows in the first round. We want to find the expected number of bullseyes she can expect. 2. **Formula used:** For a Bernoulli process with $n$ trials and success probability $p$, the expected number of successes $E(X)$ is given by: $$E(X) = n \times p$$ This formula comes from the linearity of expectation and the fact that each trial is independent. 3. **Calculation:** Here, $n = 72$ and $p = 0.75$. So, $$E(X) = 72 \times 0.75$$ 4. **Intermediate step showing multiplication:** $$E(X) = \cancel{72} \times 0.75 = 54$$ 5. **Interpretation:** Anna can expect to hit the bullseye about 54 times out of 72 shots in the first round. **Final answer:** Anna can expect approximately **54** bullseyes in the first round of 72 shots.