The binomial distribution

Compare five draws from a bag of five red and five blue counters, first replacing each counter and then keeping it out. In each case, decide whether the count of red counters has a binomial model. Explain what happens to independence and the probability of success after the first draw.

Next compare B(10,0.5) with B(20,0.25) using a graphing tool. Both means are 5, but their variances are 2.5 and 3.75. Predict which distribution is more spread out, then compare the plotted probability masses. Find a mode by comparing candidate counts with their neighbours; use unrounded probabilities when checking for a tie.