Question

you pick a card at random from an ordinary deck of 52 cards. if the card is an ace, you get 9 points, if not, you lose 1 point. what is the expected value? should you play the game? 3/13 points, yes, you should play the game 0 points, yes, the game is fair and you should play -3/13 points, no, you should not play the game write the equation for the expected value ( e(v)=\frac{4}{52}(a)+\frac{b}{52}(c) ) a = b = 48 c =

Explanation:

Step1: Identify probabilities and values

The probability of picking an ace is $\frac{4}{52}=\frac{1}{13}$, and in this case the value is $9$ points. The probability of not - picking an ace is $\frac{48}{52}=\frac{12}{13}$, and the value is $- 1$ point.

Step2: Use the expected - value formula

The expected - value formula is $E(X)=\sum_{i}p_ix_i$. Here, $E(X)=\frac{4}{52}\times9+\frac{48}{52}\times(-1)$.

Step3: Calculate the expected value

$E(X)=\frac{36}{52}-\frac{48}{52}=\frac{36 - 48}{52}=-\frac{12}{52}=-\frac{3}{13}$ points.

Answer:

Since the expected value is $-\frac{3}{13}$ points, no, you should not play the game.