Question Video: Finding a Probability Using Simple Random Sampling | Nagwa Question Video: Finding a Probability Using Simple Random Sampling | Nagwa

Question Video: Finding a Probability Using Simple Random Sampling Mathematics • First Year of Preparatory School

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Imagine that you own a movie theater and you are planning a special horror-movie film festival next month. To decide which horror movies to show, you survey moviegoers asking them which of the listed movies are their favorites. To create the list of movies needed for your survey, you decide to sample 50 of the 1,000 best horror movies of all time. What is the probability that a certain movie is selected (same for each horror movie)?

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Video Transcript

Imagine that you own a movie theater and you’re planning a special horror-movie film festival next month. To decide which horror movies to show, you survey moviegoers asking them which of the listed movies are their favorites. To create the list of movies needed for your survey, you decide to sample 50 of the 1,000 best horror movies of all time. What is the probability that a certain movie is selected, same for each horror movie?

In this example, we’re asked to find the probability that a certain movie is selected for the list of horror movies needed for the survey. To do this, let’s extract the relevant information from the question. The first thing to note is that we want to create a list of movies for the survey. Secondly, we note that the list will contain a sample of 50 of the best 1,000 horror movies of all time. So we’re going to select 50 out of a total of 1,000 movies. We’re told that the probability will be the same for each horror movie. This tells us that our sampling method in selecting the 50 movies will be simple random sampling. That’s because in a simple random sample, every member of the population must have an equal chance of selection.

The probability that a particular movie is selected at random for the sample out of the population of 1,000 movies is then given by the sample size divided by the total population. In our case, the required sample size is 50, so the probability a certain movie is selected is 50 over 1,000. As a decimal, this is equal to 0.05. Hence, the probability that a certain movie is selected for the sample of 50 from 1,000 movies is 0.05.

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