A standard deck of cards has 52 total cards divided evenly into 4 suits - there are 13 clubs, 13 diamonds, 13 hearts, and 13 spades.Ayana and Emil are playing a game that involves drawing 2 cards from a standard deck without replacement to start the game. If neither of the cards are spades, then Ayana goes first. Otherwise, Emil goes first.Is this a fair way to decide who goes first? Why or why not?Choose 1 answer:(A) No, there is a higher probability that Ayana goes first.B No, there is a higher probability that Emil goes first.(C) Yes, they both have an equal probability of going first.
Q. A standard deck of cards has 52 total cards divided evenly into 4 suits - there are 13 clubs, 13 diamonds, 13 hearts, and 13 spades.Ayana and Emil are playing a game that involves drawing 2 cards from a standard deck without replacement to start the game. If neither of the cards are spades, then Ayana goes first. Otherwise, Emil goes first.Is this a fair way to decide who goes first? Why or why not?Choose 1 answer:(A) No, there is a higher probability that Ayana goes first.B No, there is a higher probability that Emil goes first.(C) Yes, they both have an equal probability of going first.
Calculate Probability: Calculate the probability that neither of the two cards drawn are spades.Since there are 39 non-spade cards in a standard deck of 52 cards, the probability that the first card drawn is not a spade is 5239.After drawing one non-spade card, there are 38 non-spade cards left out of 51 total cards. So, the probability that the second card drawn is also not a spade is 5138.The combined probability that both cards are not spades is the product of the two probabilities:(5239)×(5138).
Perform Calculation: Perform the calculation from Step 1.(5239)×(5138)=(43)×(5138)=204114=10257.This is the probability that Ayana goes first.
Calculate Probability: Calculate the probability that at least one of the two cards drawn is a spade, which means Emil goes first.Since the probability that Ayana goes first is 10257, the probability that Emil goes first is 1−(10257).
Perform Calculation: Perform the calculation from Step 3.1−10257=102102−10257=10245.This is the probability that Emil goes first.
Compare Probabilities: Compare the probabilities to determine if the game is fair. If the probabilities were equal, then the game would be fair. However, the probability that Ayana goes first 10257 is higher than the probability that Emil goes first 10245.
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