Problem 4: Gwendolyn and Cecily are using some cards to resolve an issue: whether their absent, mutual friend Algernon is Bunburying (Gwendolyn thinks he is). The decision protocol works as follows. Gwendolyn has 4 cards with the numbers 0, 1, 2, 3 printed on them. Cecily has 4 cards with the numbers 1, 2, 3, 4 printed on them. Gwendolyn selects three cards at random from her 4 cards, then discards the high card and the low card. The remaining card is her chosen card. For example: if 0, 2, 3 is selected, the 0 and the 3 are discarded leaving the 2 as the chosen card. Cecily does the same thing except that she discards the two highest cards. For example: if 1, 2, 3 is selected, the 2 and the 3 are discarded leaving the 1 as her chosen card. Gwendolyn and Cecily then compare cards. Whoever holds the higher of the two card wins the dispute. In case of a tie, the procedure is repeated until a winner is declared. Assume that each repetition is independent of all previous plays. Part 4a: Do Gwendolyn and Cecily have an equal chance of winning on the first play? Part 4b: On average how many ties will occur before a winner is decided? Problem 4: Gwendolyn and Cecily are using some cards to resolve an issue: whether their absent, mutual friend Algernon is Bunburying (Gwendolyn thinks he is). The decision protocol works as follows. Gwendolyn has 4 cards with the numbers 0, 1, 2, 3 printed on them. Cecily has 4 cards with the numbers 1, 2, 3, 4 printed on them. Gwendolyn selects three cards at random from her 4 cards, then discards the high card and the low card. The remaining card is her chosen card. For example: if 0, 2, 3 is selected, the 0 and the 3 are discarded leaving the 2 as the chosen card. Cecily does the same thing except that she discards the two highest cards. For example: if 1, 2, 3 is selected, the 2 and the 3 are discarded leaving the 1 as her chosen card. Gwendolyn and Cecily then compare cards. Whoever holds the higher of the two card wins the dispute. In case of a tie, the procedure is repeated until a winner is declared. Assume that each repetition is independent of all previous plays. Part 4a: Do Gwendolyn and Cecily have an equal chance of winning on the first play? Part 4b: On average how many ties will occur before a winner is decided