The unconditional probability of event A is 1/2. The unconditional probability of event B is 1/3. Say whether each of the following is true or false, and explain briefly.

(a) The chance that A and B both happen must be 1/2 x 1/3 = 1/6.

(b) If A and B are independent, the chance that they both happen must be 1/2 x 1/3 = 1/6.

(c) If A and B are mutually exclusive, the chance that they both happen must be 1/2 x 1/3 = 1/6.

(d) The chance that at least one of A or B happens must be 1/2 + 1/3 = 5/6.

(e) If A and B are independent, the chance that at least one of them happens must be 1/2 + 1/3 = 5/6.

(f) If A and B are mutually exclusive, the chance that at least one of them happens must be 1/2 + 1/3 = 5/6. plo88