NBC is introducing two new television shows this season. It estimates that “Live,” a reality show in which 12 contestants vie for the affections of Justin Timberlake’s cousin, Russell, has a 60% chance of being a hit. The other show, “Inside,” a look at the seamier side of the wholesale poultry business, is given a 30% chance of being a hit. The likelihood that both will be a hit is put at 10%.
a. What is the probability that at least one of the shows will be a hit?
b. What is the probability that neither show will be a hit?
c. If Inside turns out to be a hit, how likely is it that Live will also be a hit?
d. Show a Venn diagram to represent the situation.