Question 3 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
In a game of darts, there are 20 sectors on a target, and a smaller circular "bullseye" in the center. In this particular game, a player must correctly call "low,” consisting of the sectors numbered 1–10; "high,” consisting of the sectors numbered 11–20; or "bullseye,” depending on what they are trying to hit. If they hit the section they call, they are a winner. A player will attempt to hit "low" on the first throw, then will attempt to hit "high" on the second throw, then will attempt to hit "bullseye" on the third throw, and so on until hitting the section they called.
Answer
A
Yes, the geometric distribution is appropriate.
B
No, each trial is not independent of the other trials.
C
No, it is not looking for the first occurrence of success.
D
No, the probability of success is not the same for each of the trials.
Explanation
A geometric distribution requires the probability of success to stay the same on every trial. Here, the player alternates among calling “low,” “high,” and “bullseye,” which are regions of different sizes and therefore have different probabilities of being hit. So the probability of success changes from throw to throw, making “No, the probability of success is not the same for each of the trials” the correct choice.
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