Here's the problem I have: The probability that an apple is red is 80%. The probability that a red apple is rotten is 10%. If 10 apples are picked at random, what are the odds that half are red and rotten? **Approach 1:** The odds of an apple being both red and rotten is 8%. Therefore, we have a binomial distribution with 10 trials, 5 expected successes, and probability of success 0.08. This gives us a probability of 0.054%. **Approach 2:** We would expect, on average, to get 8 red apples when we pick 10. This allows us to skip the 80% and compute a binomial distribution with the following: 8 trials, 5 expected successes, and probability 0.1. Here, we get a probability of 0.041% I believe the right answer comes from Approach 1, but I'm not sure. *Which one is correct and why do we get different numbers?*