Consider the following card game with a well-shuffled deck of cards. If you draw a red card, you win nothing. If you get a spade, you win $7. For any club, you win $10 plus an extra $21 for the ace of clubs. Let X; denote the possible winnings in this scenario. Red Card Spade X1 X2 P(X = X;) P(X = X1) P(X = X2) P( Find the following: %3D X2 = X3 = X4 = P(X = X1) = P(X = X2) = P(X = X3) P(X = X4) %3D How much should one pay to play so this game breaks even?

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Chapter8: Sequences, Series,and Probability
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Ace of clubs wins
Consider the following card
game
with a well-shuffled deck of cards. If
you draw a red card, you win
nothing. If you get a spade, you win
$7. For any club, you win $10 plus
an extra $21 for the ace of clubs. Let
X; denote the possible winnings in
this scenario.
n
Red Card
Spade
X1
X2
P(X = X;)\P(X = X1) P(X = X2)P(
Find the following:
%3D
A.
X2 =
X3 =
X4 =
Р(X — X)
P(X = X2) =
Р(X %— Хз) —
P(X = X4)
How much should one pay to
play
so this game breaks even?
Transcribed Image Text:Ace of clubs wins Consider the following card game with a well-shuffled deck of cards. If you draw a red card, you win nothing. If you get a spade, you win $7. For any club, you win $10 plus an extra $21 for the ace of clubs. Let X; denote the possible winnings in this scenario. n Red Card Spade X1 X2 P(X = X;)\P(X = X1) P(X = X2)P( Find the following: %3D A. X2 = X3 = X4 = Р(X — X) P(X = X2) = Р(X %— Хз) — P(X = X4) How much should one pay to play so this game breaks even?
Expert Solution
Step 1

Given information:

A card game consisting of a deck of well-shuffled N = 52 cards is considered.

Drawing a red card results in zero winnings.

Drawing spade results in $7 winnings.

Drawing club results in $10 winnings.

Drawing an ace of club results in $21 winnings.

It is required to obtain various probabilities of various events associated with this game.

Also, to determine how much one should pay to play this game break even.

 

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