Question

John Stockton (number 12, retired, Utah Jazz, Gonzaga University) makes 38.4% of his three-point attempts. In a game against the New York Knickerbockers, he had 3 three-point attempts. Construct a tree diagram listing all possible outcomes and the associated probabilities. What is the probability that John Stockton makes exactly two of his three attempts?

Answer 1

To construct a tree diagram, list all possible outcomes and their probabilities. The probability that John Stockton makes exactly two of his three attempts is 28.8%.

Step-by-step explanation:

To construct a tree diagram for this problem, we start with the first three-point attempt and list all possible outcomes - make or miss. For the first attempt, there are two possibilities, make or miss. These two branches then split into two more branches for the second attempt, since the outcome of the first attempt does not affect the second.

So, for the second attempt, there are four possibilities: MM (make, make), MM (make, miss), MM (miss, make), MM (miss, miss). Finally, each of these four branches splits into two more branches for the third attempt, resulting in a total of eight possible outcomes: MMM, MMM, MM, MM, MM.

Now we need to calculate the probability associated with each outcome. Since John Stockton makes 38.4% of his three-point attempts, the probability of making a three-point shot is 0.384. Therefore, for the outcomes with two makes and one miss, the probability is (0.384)^2 * (1 - 0.384) = 0.096. There are three such outcomes: MMM, MMM, and MM (miss, make, make). So the final probability is 3 * 0.096 = 0.288, or 28.8%.