The weather forecast says there is a 40% chance of rain today and a 30% chance of rain tomorrow. Assume the days are independent. (a) What is the chance of rain on both days? (b) What is the chance of...

The weather forecast says there is a 40% chance of rain today and a 30% chance of rain tomorrow. Assume the days are independent.

(a) What is the chance of rain on both days?

(b) What is the chance of rain on neither day?

(c) What is the chance of rain on at least one day?

The following is a probability distribution of the number of defects on a given contact lens produced in one shift on a production line:

Let A be the event that one defect occurred, and B be the event that 2, 3, or 4 defects occurred. Find:

(a) P(A) and P(B)

(b) P(A and B)

(c) P(A or B)