3. Tony runs a pie stand that sells two types of pie outside a football ground. He wants to estimate the probability that a customer will buy a steak pie rather than a vegetable pie. He conducts a survey by randomly selecting customers and recording their choice of pie. When he feels he has enough data, he notes that 55 customers bought steak pies and 25 bought vegetable pies.

1. Calculate an approximate \(90 \%\) confidence interval for \(p\), the probability that a randomly selected customer buys a steak pie.
2. Suppose that Tony carries out 50 such surveys and calculates \(90 \%\) confidence intervals for each survey. Determine the expected number of these confidence intervals that would contain the true value of \(p\).