Find the probabilities and indicate when the “5% guideline...

Find the probabilities and indicate when the “5% guideline for cumbersome calculations” is used. In a Microsoft Instant Messaging survey, 1021 adults were asked to identify the most fun way to flirt, and 61 of them chose email. a. If 1 of the surveyed adults is randomly selected, what is the probability that this person chose something other than email? b. If 40 of the different subjects are randomly selected without replacement, what is the probability that each of them chose something other than e- mail?

Find the probabilities and indicate when the “5% guideline for cumbersome calculations” is used.
In a Microsoft Instant Messaging survey, 1021 adults were asked to identify the most fun way to flirt, and 61 of them chose email.
a. If 1 of the surveyed adults is randomly selected, what is the probability that this person chose something other than email?
b. If 40 of the different subjects are randomly selected without replacement, what is the probability that each of them chose something other than e-
mail?

Key Concepts

Complementary Probability

This concept involves finding the probability that an event does not occur by subtracting the probability of the event from 1. In the given problem, instead of directly calculating the probability of not choosing email, you can compute it as 1 minus the probability of choosing email. This simplifies many problems where calculating the complement is more straightforward than calculating the event directly.

Sampling Without Replacement

This principle addresses situations where selections are made from a finite population and after each selection, the population size decreases. Because the probability of subsequent selections can change after each draw, the events are dependent. However, if the sample is small relative to the population, the dependency can often be ignored for approximation purposes.

Multiplication Rule for Dependent Events

This rule is used to calculate the joint probability of several events occurring in sequence when the events influence each other, as they do in sampling without replacement. It requires multiplying the probability of each event by the conditional probability of the subsequent event, given the preceding events have occurred.

5% Guideline

The 5% guideline is used as a rule of thumb to decide if the dependency between selections in sampling without replacement is negligible. When the sample size is less than 5% of the overall population, the probability change is usually minimal, allowing one to assume independence, which simplifies calculations by using the multiplication rule as if the events were independent.

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