In Major League Baseball, each team plays 162 games in the regular season. A winning streak is a run of at least two wins sandwiched by losses (except for the winning streak that begins from game 1, or the winning streak that ends in game 162). For instance, the record WLLWWWLWLWWW consists of 2 winning streaks (games 4-6 and games 10-12). Suppose that Oakland A's baseball team will win each game with probability p = 0.55, independent of previous games (there is no tie in Major League Baseball). What is their expected number of winning streaks in a season?

John can take one of two highways, Interstate A and Interstate B, to get to work each day. The probability that there will be a traffic jam on Interstate A on a given day is 0.65, and the probability that there will be a traffic jam on Interstate B is 0.2. The probability that there will be a traffic jam on at least one of Interstate A or Interstate B is 0.8. Determine the probability that both Interstate A and B will be congested. 0.235 None in the list 0.050 0.062 0.765 Submit Answer Tries 0/3 Determine the probability that Interstate B is congested given that Interstate A is congested. 0.250 0.077 0.812 0.062 None in the list Submit Answer Tries 0/3 Determine the probability that there is a traffic jam on Interstate A given that at least one of the Interstates has a traffic jam. 0.062 None in the list 0.250 0.812 0.077

Butch has a collection of 60 vinyl records from throughout the 20th century including seven from the 40s, eight from the 50s, seven from the 60s, six from the 70s, and 12 from the 80s. If he randomly selects one from his collection of 60, find the probability it will be from each of the following decades.

Suppose that you repeatedly roll a pair of fair dice and keep track of the sum. What is the probability that you see a sum of 7 before you see an even sum 3 times? (In particular, you keep track of how many evens you roll, and you want the probability that you roll a 7 before you get to 3 evens.