Players in sports are said to have \"hot streaks\" and \"cold streaks.\" For exa
ID: 3276849 • Letter: P
Question
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 that player has made 10 outs in 10 consecutive at-bats. Suppose that a hitter successfully reaches base 35% of the time he comes to the plate. Complete parts (a) through (c) below. Find the probability that the hitter makes 10 outs in 10 consecutive at-bats, assuming at-bats are independent events. Hint: The hitter makes an out 65% of the time.
a. P(hitter makes 10 consecutive outs) =
b. Are cold streaks unusual?
c. Interpret the probability from part a.
In repeated sets of 10 consecutive at-bats, the hitter is expected to make an out in all 10 at-bats about 18 times out of 1000.
Explanation / Answer
a) Probability that he makes 10 consecutive outs is computed as:
= 0.65*0.65*0.65.........10 times
= 0.6510
= 0.0135
Therefore 0.0135 is the required probability here.
b) Cold streaks could be unusual because they happen only 1.35% of the time as seen from the above computed probability.
c) As the events are independent, therefore we used the multiplication rule to get the probability of 10 consecutive same events.
In repeated sets of 10 consecutive at bats, the hitter is expected to make an out in all 10 at bats about 14 times out of 1000.