Question

Marshall spins a prize wheel with 4 segments of equal size, one of which is labeled "winner." let x = the number of spins until marshall wins a prize. check the conditions to determine if this is a geometric setting.

1. are the outcomes binary? success/failure:

Answer 1

Marshall's prize wheel scenario is a geometric setting because it meets the conditions for a geometric distribution: binary outcomes (win or not win), constant probability of success (1/4), and independent trials.

Step-by-step explanation:

Marshall is involved in a situation that can be described as a geometric setting because of certain conditions that are met. In geometric probability, we are often interested in the number of trials needed to achieve the first success. Here, spinning the prize wheel until he wins (considered a 'success') follows a geometric distribution, as each spin is an independent event with two possible outcomes (winning or not winning), and the probability of winning remains constant at 1/4 with each spin.

The geometric setting checks the following conditions:

• The outcomes are binary, which means they are either a success (winning) or a failure (not winning).
• The probability of success (p) is constant; in this case, p=1/4, since there is one winning segment out of four.
• The trials are independent, meaning the outcome of one spin does not affect the outcome of another.

Therefore, the variable x, which represents the number of spins until Marshall wins, is indeed a geometric random variable.