Question

The odds of dying of heart disease/cancer are 1 in 7. Determine the probability that in a group of 3 people, none of them die from heart disease or cancer. Explain how you came to your answer. Finally, determine the probability that in a group of 3 people, at least one of them die from heart disease or cancer, and explain why it is so difficult to calculate this probability directly yet so easy to calculate it using a trick.

Answer 1

If we calculate the probability of P(X>=1) directly, we need to calculate the probability for X=1, X=2, and X=3. Instead, using this small trick of subtracting P(X=0) from 1, we get the desired result easily