Question

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. Clubs and spades are black cards, while diamonds and hearts are red cards.Marquis and Sasha are playing a game that involves drawing 2 cards from a standard deck withoutreplacement to start the game. If both cards are the same color (both red or both black), then Marquis goesfirst. Otherwise, Sasha goes first.Is this a fair way to decide who goes first? Why or why not?Choose 1 answer:

Answer 1

- In order to determine whether this method of starting the game is fair or not, we simply need to calculate the probability of choosing two cards of the same color consecutively and the probability of choosing two cards of different colors consecutively.

Probability of choosing two cards of the same color consecutively:

`\begin{gathered} P(red)=(26)/(52)\text{ \lparen Since there are 26 red cards out of 52\rparen} \\ \\ P(black)=(26)/(52)\text{ \lparen Since there are 26 black cards out of 52\rparen} \\ \\ \text{ Choosing two red cards consecutively and choosing two black cards } \\ \text{ consecutively is the same. } \\ \\ P(red\text{ twice})=P(red\text{ first time})\text{ AND }P(red\text{ second time\rparen} \\ P(red\text{ twice\rparen}=(26)/(52)*(25)/(51)=(25)/(102) \end{gathered}`

Probability of choosing two cards of the different colors consecutively:

`\begin{gathered} \text{ The probability of choosing a red card first and then a black card is the same} \\ \text{ as choosing a black card first and then a red card.} \\ \\ P(red\text{ AND then black\rparen}=P(red\text{ first})* P(black\text{ second\rparen} \\ P(red\text{ AND then black})=(26)/(52)*(26)/(51)=(26)/(102) \\ \end{gathered}`

- Now we can see that:

[tex]P(red\text{ twice\rparen}

- This implies that the method of starting the game is not fair

- Thus, there is a higher chance that Sasha starts first.

Final Answer

The answer is OPTION B