Question

In a recent basketball season, Jenny sunk a three-point shot once in every 3.2 attempts, on average. Assume that this probability did not change going into the next season. What is the probability that Jenny sinks her first three-point shot on her second attempt of the season? Use a TI-83, TI-83 Plus, or TI-84 calculator to find the probability.

Round your answer to three decimal places.

Answer 1

The probability that Jenny sinks her first three-point shot on her second attempt is 0.215 when rounded to three decimal places.

Step-by-step explanation:

The question is asking for the probability that Jenny sinks her first three-point shot on her second attempt. To solve this, we use the geometric distribution. The probability p of success on a single trial (sinking a three-point shot) is the reciprocal of the average number of attempts per success, so p = 1/3.2 = 0.3125. The probability q of failure (not sinking a shot) is 1 - p = 1 - 0.3125 = 0.6875.

Since the question is asking for Jenny to miss the first shot and then make the second shot, we multiply q by p: 0.6875 * 0.3125. Using a TI-83, TI-83 Plus, or TI-84 calculator, this calculation gives us:

Probability on second attempt = 0.6875 * 0.3125 = 0.21484375

Rounded to three decimal places, the probability is 0.215.