Election day is less than a month away, and political analysts are focused on the races for two statewide political offices. according to a recent poll, in the race for governor, 40% of voters support the republican candidate and 53% of voters support the democratic candidate. in the race for attorney general, 61% of voters support the republican candidate and 37% of voters support the democrat. assume that voter preference of candidate for each of the two offices is independent of each other.

what is the probability that a randomly selected voter supports both the democratic candidate for governor and the democratic candidate for attorney general?

what is the sample space for all of the possible outcomes in voter support of the candidates for governor and attorney general?

a set of outcomes (a subset of the sample space) is called an event.

which outcomes from the sample space are in the event, supporting “democratic governor”? which outcomes are in the event, supporting “democratic attorney general”?

the intersection of two events a and b is the event consisting of all outcomes that are in both a and b.

if you have not done so already, create an area model for this situation. what outcomes are in the intersection of the events “democratic governor” and “democratic attorney general”? how can this be seen in your area model?

shade your area model to highlight the event “democratic governor”. then shade your area model to highlight the event “democratic attorney general”. what do you notice about the intersection of the events?