In the last round of a chess tournament the final match is between Alice and Diego. The winner is the first player to win three games [sometimes called "best of 5"]. Assume that they are equally matched, so that each player has an equal probability of winning each game. What is the probability that the match will be finished after the first 3 games are played?

The average number of vehicles waiting in line to enter a parking lot can be modeled by the function f left parenthesis x right x squared over 2 left parenthesis 1 minus x right parenthesis endfraction , where x is a number between 0 and 1 known as the traffic intensity. find the rate of change of the number of vehicles waiting with respect to the traffic intensity for the intensities (a) xequals0.3 and (b) xequals0.6.