For the mayors in Problem 9.58, 15 of the 40 women are...

Name: Problem 59, Chapter 9: Schaum's Outline of Elements of Statistics I: Descriptive Statistics and Probability
Uploaded: 2021-06-11T14:22:55-08:00
Duration: 2 min 7 s
Channel: Christopher Stanley
Description: For the mayors in Problem 9.58, 15 of the 40 women are Republicans. If cene mayor is randomly selected from all 100 mayors each day for two days (sampling with replacement), then detemine the probability that (a) a man will be chosen on day one and a woman on day two, (b) on day two, either a male Democrat or a female Republican will be chosen.

For the mayors in Problem 9.58, 15 of the 40 women are Republicans. If cene mayor is randomly selected from all 100 mayors each day for two days (sampling with replacement), then detemine the probability that (a) a man will be chosen on day one and a woman on day two, (b) on day two, either a male Democrat or a female Republican will be chosen.

Key Concepts

Addition Rule

The addition rule is used when calculating the probability of either one event or another occurring, especially when these events are mutually exclusive (i.e., they cannot both occur at the same time). In part (b) of the problem, the probability of selecting a mayor that meets one condition or the other is determined by adding the individual probabilities of these non-overlapping outcomes.

Sampling With Replacement

Sampling with replacement is a process in which each item selected is returned to the population before the next selection is made. This keeps the probabilities constant for each selection, ensuring that each draw is an independent event and simplifying the calculation of combined probabilities.

Multiplication Rule

The multiplication rule is used to find the probability of two independent events both occurring by multiplying their individual probabilities. For instance, the probability of selecting a mayor with a specific gender on day one and another with a different characteristic on day two is the product of the separate probabilities for each day.

Probability

Probability is the measure of how likely an event is to occur, usually expressed as a ratio of the number of favorable outcomes to the total number of possible outcomes. In problems like this, probability helps us quantify the chance of selecting a mayor with a specific characteristic on any given day.

Independent Events

When two events are independent, the occurrence of one does not affect the probability of the other. In the context of sampling with replacement, each selection is independent because the composition of the population remains unchanged from day to day.

Transcript

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