Consider a mediocre basketball player who has consistently made only 50% of his free throws over several seasons. If we were to examine his free throw record over the last 50 free throw attempts, is it likely that we would see a streak of 5 in a row where he is successful in making the free throw? In this activity, we will investigate this question. We will assume that the outcomes of successive free throw attempts are independent and that the probability that the player is successful on any particular attempt is .5.

1. Begin by simulating a sequence of 50 free throws for this player. Because this player has probability of success of .5 for each attempt and the attempts are independent, we can model a free throw by tossing a coin. Using heads to represent a successful free throw and tails to represent a missed free throw, simulate 50 free throws by tossing a coin 50 times, recording the outcome of each toss.

2. For your sequence of 50 tosses, identify the longest streak by looking for the longest string of heads in your sequence. Determine the length of this longest streak.

3. Combine your longest streak value with those from the rest of the class and construct a histogram or dotplot of these longest streak values.

4. Based on the graph from Step 3, does it appear likely that a player of this skill level would have a streak of 5 or more successes sometime during a sequence of 50 free throw attempts? Justify your answer based on the graph from Step 3.