Using the Multiplication Rule In Exercises 19-32, use the Mult...

Question

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

25. Best President In a sample of 1500 adult U.S. citizens, 270 said that Barack Obama was the best president in U.S. history. Two adult U.S. citizens are selected at random.

(Adapted from YouGov)

d. Which of the events can be considered unusual? Explain.

Accepted Answer

Welcome back, everyone. In a survey of 1200 employees, 97 said their bike to work. If two employees are chosen at random, is it unusual for both to bike to work? Explain your reasoning. A says no because the probability that both employees back to work is less than 0.05. B says yes because the probability that both employees back to work is less than 0.05. C says no because the probability that both employees bike to work is greater than 0.05, and the D says yes because the probability that both employees bike to work is greater than 0.05. No What does it mean for an event or a probability to be unusual? Well, recall, OK, that a probability. Uh, or sorry, an event recall that an event. Is is typically considered unusual. OK. If It's probability. Is less than. 0.05, OK. So if we're going to tell if this event is unusual first we need to find its probability and then compare it to our uh threshold 0.05. So what is the probability then that if two employees are chosen at random they both bike to work? Well, assuming independence here since the sample size is very small relative to the population, the probability that both employees, OK, let's put that in red here, the probability that both employees bike to work will be the product of both probabilities. OK, in other words. Here, if the first employee bikes to work, it's gonna be the number of successes 97 divided by the total number of outcomes 1200, and we're going to multiply that by the probability the second employee bikes to work, which is also 97 divided by 1200. No, this is really 97 divided by 1200 squared. And when we calculate here, we get this to be approximately 0.00653. Now how does this compare? Well, the probability then that both bikes, which is 0. or approximately. 0.00653 is less than 0.005, OK? So because it is less, that means it is indeed unusual, OK? So, it's unusual. It's it is an unusual event because the probability that both employees back to work is less than 0.05. If we look back at our answer choices, that means B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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Key Concepts

Multiplication Rule

Probability of an Event

Unusual Events

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