Question

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. is it appropriate to use the geometric distribution to calculate probabilities in this situation? yes, the geometric distribution is appropriate. no, each trial is not independent of the other trials. no, it is not looking for the first occurrence of success. no, the probability of success is not the same for each of the trials.

Explanation:

The geometric distribution is used to find the probability of the first success in a series of independent Bernoulli trials with the same probability of success \(p\) for each trial. In this dart - game situation:

• The probability of hitting "low" (success for the first trial) is \(p_1=\frac{10}{20}=\frac{1}{2}\), the probability of hitting "high" (success for the second trial) is \(p_2 = \frac{10}{20}=\frac{1}{2}\), and the probability of hitting "bullseye" (success for the third trial) is \(p_3=\frac{1}{20}\). Since \(p_1

eq p_2
eq p_3\), the probability of success is not the same for each trial.

Answer:

No, the probability of success is not the same for each of the trials.