Find the probability that you go first and your friend goes second.

Question

There are eight contestants in an obstacle course race. You and your friend are two of the contestants. Contestants run the course one at a time and the order in which the contestants run the course is chosen at random. Find the probability that you go first and your friend goes second. Write your answer as a fraction in simplest form.

Answer 1

At the start of the race there are 8 contestants with an equal chance of starting first. You have a 1 in 8 chance of being selected. Then there are 7 contestants left, and you friend has a 1 in 7 chance of going second. Both selections must happen, and are independent events, so multiply the probabilities, (1/8) x (1/7) = 1/56.

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