4.4 Exercise 7

The lifetime risk of developing cancer is about one in 67 (1.5%). Let X = the number of people you ask until one says they have cancer. Then X is a discrete random variable with a geometric distribution: $X \sim G \left(\frac{1}{67}\right)$ or $X \sim G \left(0 . 015\right)$

1. What is the probability of that you ask ten people before one says they have cancer?
2. What is the probability that you must ask 20 people?
3. Find the (i) mean and (ii) standard deviation of X.