Which describes a uniform probability model?
Responses
A selecting a day of the week using only the first letter of that dayselecting a day of the week using only the first letter of that day
B an even or odd sum from rolling two dicean even or odd sum from rolling two dice
C selecting a ball from 3 yellow balls and 2 red ballsselecting a ball from 3 yellow balls and 2 red balls
D the number of heads and tails from flipping two coins
C selecting a ball from 3 yellow balls and 2 red balls (all options are examples of probability models, but only option C describes a uniform probability model where each outcome has an equal chance of occurring).
how
In a uniform probability model, all outcomes have equal likelihood of occurring. In option C, there are 3 yellow balls and 2 red balls, so each color has a probability of 3/5 of being selected. Therefore, the probability of selecting a yellow ball is 3/5 and the probability of selecting a red ball is also 3/5, which represents a uniform probability model.
In options A, B, and D, not all outcomes have an equal likelihood of occurring. For example, in option A, the first letter of the day "T" has a probability of 1/7 of being selected, while the first letter of the day "S" has a probability of 2/7 of being selected. This does not represent a uniform probability model.
The correct answer is option A: selecting a day of the week using only the first letter of that day.
To understand why this describes a uniform probability model, we need to consider what a uniform probability model means. In a uniform probability model, each possible outcome has an equal chance of occurring.
In this case, when selecting a day of the week using only the first letter, there are seven possible choices (M for Monday, T for Tuesday, W for Wednesday, etc.). Each letter has an equal probability of being selected since they all represent days of the week.
To confirm this, you can calculate the probability of selecting each letter:
P(M) = 1/7
P(T) = 1/7
P(W) = 1/7
P(T) = 1/7
P(F) = 1/7
P(S) = 1/7
P(S) = 1/7
As you can see, the probability of selecting each letter is the same (1/7).
Therefore, option A describes a uniform probability model.