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Khan Academy Get Al Tutoring NeW [ Donate ^(x) lainey_ Google Classroom Marcus and Isabel are playing a game that involves flipping 2 fair coins to see who gets to be the "banker." The exact results determine other aspects of the game, but if both coins land showing the same result (both heads or both tails), then Marcus gets to be the banker. If the coins show different results from each other (one shows heads while the other shows tails), then Isabel gets to be the banker. Is this a fair way to decide who gets to be the banker? Why or why not? Choose 1 answer: (A) No, Marcus is most likely to be banker. B No, Isabel is most likely to be banker. C Yes, they both have an equal probability of being the banker. Stuck? Review related articles/videos or use a hint. 4 of 4

Khan Academy\newlineGet Al Tutoring\newlineNeW\newline[\newlineDonate x { }^{x} \newlinelainey_\newlineGoogle Classroom\newlineMarcus and Isabel are playing a game that involves flipping 22 fair coins to see who gets to be the

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Q. Khan Academy\newlineGet Al Tutoring\newlineNeW\newline[\newlineDonate x { }^{x} \newlinelainey_\newlineGoogle Classroom\newlineMarcus and Isabel are playing a game that involves flipping 22 fair coins to see who gets to be the
  1. Determine Possible Outcomes: Determine the possible outcomes when flipping two fair coins.\newlineThere are 44 possible outcomes when flipping two coins:\newline11. Both coins land on heads (HH).\newline22. Both coins land on tails (TT).\newline33. One coin lands on heads and the other on tails (HT).\newline44. One coin lands on tails and the other on heads (TH).
  2. Calculate Marcus' Probability: Calculate the probability of Marcus becoming the banker.\newlineMarcus becomes the banker if both coins show the same result. There are two favorable outcomes for Marcus: HH and TT.\newlineThe probability of Marcus becoming the banker is the number of favorable outcomes for Marcus divided by the total number of outcomes.\newlineProbability (Marcus) = Number of favorable outcomes for MarcusTotal number of outcomes\frac{\text{Number of favorable outcomes for Marcus}}{\text{Total number of outcomes}}\newlineProbability (Marcus) = 24\frac{2}{4}\newlineProbability (Marcus) = 12\frac{1}{2}
  3. Calculate Isabel's Probability: Calculate the probability of Isabel becoming the banker.\newlineIsabel becomes the banker if the coins show different results. There are two favorable outcomes for Isabel: HT and TH.\newlineThe probability of Isabel becoming the banker is the number of favorable outcomes for Isabel divided by the total number of outcomes.\newlineProbability (Isabel) = Number of favorable outcomes for IsabelTotal number of outcomes\frac{\text{Number of favorable outcomes for Isabel}}{\text{Total number of outcomes}}\newlineProbability (Isabel) = 24\frac{2}{4}\newlineProbability (Isabel) = 12\frac{1}{2}
  4. Compare Probabilities: Compare the probabilities to determine if the game is fair.\newlineSince the probability of Marcus becoming the banker is 12\frac{1}{2} and the probability of Isabel becoming the banker is also 12\frac{1}{2}, both players have an equal chance of becoming the banker.\newlineTherefore, the method of deciding who gets to be the banker is fair.

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