Susie is looking for butterflies in an area where:

15% of the butterflies are of type A

20% of the butterflies are of type B

65% of the butterflies are of type C

Suppose that she spots two butterflies on her walk, and that the types of the two butterflies are independent from each other (perhaps because they are spotted in different locations).

(a) What is the probability that the two butterflies she spots will both be type A butterflies?

(b) What is the probability that the two butterflies she spots will be of the same type?

(c) What is the probability that neither of the two butterflies she spots will be type C butterflies?

A survey is being conducted in a county where 58% of the voters are Democrats and 42% are Republican.

(c) What is the probability that one would be a Democrat and one a Republican?

Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. For each game they play, the probability that the Bears win is 0.6 and the probability the Wildcats win is 0.4.

(e) What is the probability that the Bears win the series in exactly 5 games? 

(f) What is the probability that the Wildcats win the series in exactly 5 games? 

(g) What is the probability that the Bears win the series (i.e. the Bears win but we don't care how many games are required)? 

(h) What is the probability that the Wildcats win the series?