In the cold-vaccination study described in Example 9.1, 100...

Name: Problem 9, Chapter 9: Schaum's Outline of Elements of Statistics I: Descriptive Statistics and Probability
Uploaded: 2022-04-04T08:39:01-08:00
Duration: 1 min
Channel: Varsha Aggarwal
Description: In the cold-vaccination study described in Example 9.1, 100 people got colds and 60 people did not get colds (see Table 9.1). Four consecutive random selections are made from the 160 people, with replacement after each selection. What is the probability that the first two had colds and the second two did not?

In the cold-vaccination study described in Example 9.1, 100 people got colds and 60 people did not get colds (see Table 9.1). Four consecutive random selections are made from the 160 people, with replacement after each selection. What is the probability that the first two had colds and the second two did not?

Key Concepts

Independent Events

Independent events are those whose outcomes do not affect each other. In the context of sampling with replacement, each draw is independent because the result of one draw does not alter the probabilities for the subsequent draws, allowing us to treat each selection as having the same fixed probability.

Multiplication Rule

The multiplication rule in probability is used to compute the likelihood of a sequence of independent events occurring. It states that the overall probability is the product of the individual probabilities. In scenarios like the four consecutive selections in the study, the overall probability is calculated by multiplying the probability of each individual event.

Probability

Probability is the measure of the likelihood that an event will occur. In problems like the cold-vaccination study, probabilities are calculated by taking the ratio of favorable outcomes to the total number of outcomes, which in this context involves determining the chance a randomly selected person falls into a specific category (e.g., got a cold or did not get a cold).

Sampling with Replacement

Sampling with replacement is a method where each selected individual is returned to the population before the next draw. This means that the probability for each selection remains constant and the selections are independent of each other, as the total number of individuals remains unchanged between draws.

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