Corey and Yin are trying to decide who will get to choose where they go for lunch. They decide to flip a coin until it lands showing heads. If the first flip shows heads, then Corey gets to choose. If heads shows on the second flip or later, then Yin gets to choose. Is this a fair way to decide who chooses where they go lunch? Why or why not? Choose 1 answer: A No, Corey is most likely to get to choose. (B) No, Yin is most likely to get to choose. C Yes, they both have an equal probability of choosing.

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Define Events C and Y: Let's define the event where Corey gets to choose as ＂C＂ and the event where Yin gets to choose as ＂Y＂. We need to calculate the probability of each event to determine if the method is fair.Calculate Probability of Event C: The probability of the coin landing on heads on the first flip (event C) is 1/2, since there are two possible outcomes (heads or tails) and the coin is fair.Calculate Probability of Event Y: The probability of the coin landing on tails on the first flip and heads on the second flip (event Y) is (1/2) * (1/2) = 1/4, since the events are independent and each has a probability of 1/2.Consider Infinite Series of Probabilities: However, event Y also includes all scenarios where the coin lands on tails any number of times before finally landing on heads on any flip after the first. This means we need to consider an infinite series of probabilities: (1/2) * (1/2) for the second flip, (1/2) * (1/2) * (1/2) for the third flip, and so on.Calculate Probability of Yin Choosing: The probability of Yin getting to choose is the sum of the probabilities of the coin landing on heads on the second flip or later. This is a geometric series with the first term a = (1/2) * (1/2) = 1/4 and the common ratio r = 1/2. The sum of an infinite geometric series is given by S = a / (1 - r).Determine Fairness of Method: Substituting the values of a and r into the formula, we get S = (1/4) / (1 - (1/2)) = (1/4) / (1/2) = 1/2. This means the probability of Yin getting to choose is 1/2.Since the probability of Corey getting to choose is also 1/2, and the probability of Yin getting to choose is 1/2, the method is fair because both Corey and Yin have an equal probability of 1/2 of getting to choose where they go for lunch.

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