Players in sports are said to have “hot streaks” and “cold streaks.” For example, a batter in baseball might be considered to be in a slump, or cold streak, if he has made 10 outs in 10 consecutive at-bats. Suppose that a hitter successfully reaches base 30% of the time he comes to the plate.
(a) Find and interpret the probability that the hitter makes 10 outs in 10 consecutive at-bats, assuming that at-bats are independent events.
(b) Are cold streaks unusual?
(c) Find the probability the hitter makes five consecutive outs and then reaches base safely.