N = {May, Jun, Jul, Aug}, L = {Jan, Mar, May, Jul, Aug, Oct, Dec}, and N ∩ L = {May, Jul, Aug}. Three out of seven outcomes of L belong to N as well, so P(N |L)=3/7. 2. The event A is contained in C....

N = {May, Jun, Jul, Aug}, L = {Jan, Mar, May, Jul, Aug, Oct, Dec}, and N ∩ L = {May, Jul, Aug}. Three out of seven outcomes of L belong to N as well, so P(N |L)=3/7.

2. The event A is contained in C. So when A occurs, C also occurs; therefore P(C | A) = 1. Since Cc = {123, 321} and A ∪ B = {123, 321, 312, 213}, one can see that two of the four outcomes of A ∪ B belong to Cc as well, so P(Cc | A ∪ B)=1/2.