Ace of clubs wins. Consider the following card game with a

Step 1 of 3

(a) A deck of cards contains 52 cards, in which 13 suit 26 red cards and 26 black cards. There are 4 sets with denominations A, 2, 3, …..10, J, Q and K. In these J, Q and K are face cards.

X = amount you can win at this game (Dollars you can win)

x = (0, 5, 10, 20)

\(\begin{array}{l} P(X=0)=P(\text { probability of picking a red card })=\frac{26}{52}=0.50 \\ P(X=5)=P(\text { probability of picking a spade })=\frac{13}{52}=0.25 \\ P(X=10)=P(\text { probability of picking a club, but not the ace })=\frac{12}{52}=0.23 \\ P(X=20)=P(\text { Probability of picking the ace of clubs })=\frac{1}{52}=0.019 \end{array}\)

Probability Distribution of X

\(\begin{array}{|c|c|c|c|} \hline \text { Event } & x & P(X=x) & x^{*} P(x) \\ \hline \text { Red Card } & 0 & \frac{26}{52}=0.50 & 0 \\ \hline \text { Spade } & 5 & \frac{13}{52}=0.25 & 1.25 \\ \hline \text { Clubs (not the Ace) } & 10 & \frac{12}{52}=0.231 & 2.31 \\ \hline \text { Clubs } & 10+20=30 & \frac{1}{52}=0.019 & 0.57 \\ \hline \end{array}\)