Answer:
Heres all the Answer:
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.
Write the equation for the expected value.
E(V) =
4
/52
(a)
+
b
/52
(c)
a = 9
b = 48
c =
-1
What is the expected value? Should you play the game?
✔ –3/13 points; no, you should not play the game
For what expected value is a game fair?
✔ E(X) = 0
What value for the aces would make the game fair? To find this, solve the equation:
0 = 4
/52
(x) + 48
/52
(−1)
= 12 points
Step-by-step explanation:
Got it all from E D G E N U I T Y
Hope this helps ya'll :P
The equation of the expected value is [tex]E(x) = 9 * \frac{1}{13} - 1 * \frac{12}{13}[/tex]
In a standard deck of cards, there are:
Ace = 4
Cards = 52
So, the probability of selecting an ace is:
[tex]p = \frac{4}{52}[/tex]
Simplify
[tex]p = \frac{1}{13}[/tex]
The probability of not selecting an ace is calculated using the following complement rule
[tex]q = 1 - \frac{1}{13}[/tex]
Simplify
[tex]q =\frac{12}{13}[/tex]
The expected value is then calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
This gives
[tex]E(x) = 9 * \frac{1}{13} - 1 * \frac{12}{13}[/tex]
Hence, the equation of the expected value is [tex]E(x) = 9 * \frac{1}{13} - 1 * \frac{12}{13}[/tex]
Read more about expected values at:
https://brainly.com/question/15858152
