Video: Finding Probability Using Permutations

Ethan, Jacob, and three of their coworkers each take the bus to work. If they each have an equal chance of arriving first, determine the probability of Jacob arriving first and Ethan arriving second.

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Video Transcript

Ethan, Jacob, and three of their coworkers each take the bus to work. If they each have an equal chance of arriving first, determine the probability of Jacob arriving first and Ethan arriving second.

In this question, there are five people: Ethan, Jacob, and the three coworkers. We want to calculate the probability of Jacob arriving first and Ethan arriving second. As there is an equal chance of them all arriving first, the probability that Jacob arrives first is one-fifth, one out of five. As Jacob has now arrived, there are four people left to arrive: Ethan and the three other coworkers. What is the probability of Ethan arriving next?

As there are four people and Ethan is one of them, there is a one-in-four chance or a one-quarter chance of Ethan arriving second, assuming that Jacob has arrived first. As we want both of these events to happen, Jacob to arrive first and Ethan to arrive second, we need to multiply the two fractions. Therefore, the probability of Jacob arriving first and Ethan arriving second is one-fifth multiplied by one-quarter.

In order to multiply two fractions, we first multiply the numerators. One multiplied by one is equal to one. We then multiply the denominators. Five multiplied by four is 20. Therefore, one-fifth multiplied by one-quarter is equal to one 20th. This means that there is a one-in-20 chance that Jacob arrives first and Ethan arrives second.

As one 20th is equivalent to five 100ths, we could also write this as 0.05, or five percent. There is a five percent chance of Jacob arriving first and Ethan arriving second.

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