Video: Calculating Probabilities Using Permutations

Two people are chosen randomly from a group of six hundred two. What is the probability that Benjamin was selected first and Ethan second?

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Video Transcript

Two people are chosen randomly from a group of 602. What is the probability that Benjamin was selected first and Ethan second?

We can write any probability as a fraction, where the numerator is the number of successful outcomes and the denominator is the number of possible outcomes. The probability that Benjamin was selected first is one out of 602. There are 602 people in total and Benjamin is one of them. As Benjamin has now been selected, there are 601 people left. The probability that Ethan is selected second is one out of 601.

As we want both of these events to occur: Benjamin to be selected first and Ethan to be selected second, we need to multiply the two fractions. One out of 602 multiplied by one out of 601. This gives us an answer of one out of 361802.

Therefore, this is the probability that Benjamin was selected first and Ethan was selected second out of a group of 602 people.

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