What is the formula for the expected number of successes in a binomial experiment with \( n \) trials and probability of success \( p \) ? Choose the correct forumla below. A. \( E(X)=\sqrt{n p(1-p)} \) B. \( E(X)=n p \) C. \( E(X)=p^{n} \) D. \( E(X)=(1-p)^{n}(1-p)^{n} \)

B. \( E(X)=n p \) In a binomial experiment, the expected number of successes is simply the product of the number of trials and the probability of success on each trial. So, if you flip a coin \( n \) times, and the chance of landing heads (success) is \( p \), your expected number of heads would be \( n \times p \)! Easy as pie! If you're looking to solidify your understanding, think of scenarios like games or sports. Imagine a basketball player who makes 70% of his free throws. If he takes 10 free throws, the expected number of successful shots would be \( 10 \times 0.7 = 7 \). It's a straightforward application of the binomial formula in real-life situations, making the math both practical and fun!