Many species have “assortative mating,” meaning that a female is more likely to mate with a male that is similar to her in some particular feature, such as body size, than with a dissimilar male. Imagine a female butterfly weighing 0.4 g in a population where the weight of males is normally distributed with mean 0.3 g and standard deviation 0.08 g. Assume that the female encounters males independently of his body weight.

a. What is the probability that the first male she encounters is within 0.1 g of her own weight?

b. What is the probability that the first five males she encounters are all more than 0.1 g different from her in body weight?