Question 1194591: You pick a card from a deck. If it is faced card, you will win 500.00, if you get an ace, you will win 1000.00, if the card is Red you get 100.00. For any other card, you will win nothing. Find the expected value that you can possibly win.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Face Cards = {Jack, Queen, King}
We have 3 cards in any given suit, and 4 suits, so there are 3*4 = 12 face cards.
The probability of selecting a face card is
12/52 = 3/13 = 0.2308 = 23.08%
The decimal values are approximate.
I'll use the reduced fraction form when creating the table below.
The probability of an ace is
4/52 = 1/13 = 0.0769 = 7.69%
since we have 4 aces out of 52 cards total.
These decimal values are also approximate.
Half the cards are red, so 1/2 is the probability of getting a red card.
Or you could say
26/52 = 1/2 = 0.50 = 50%
There are 26 black cards.
Kick out the ace of spades and ace of clubs to get 26-2 = 24 cards left. Then kick out the face cards that are spades and clubs (2*3 = 6 total) to be left with 24-6 = 18 cards that do not fit any of the previous categories of face card, ace, or red card.
18/52 = 9/26 = 0.3462 = 34.62% is the probability of getting any other card.
The decimal values are approximate.
Here's the summary of probabilities we'll need
Face card = 3/13
Ace = 1/13
Red card = 1/2
Any other card = 9/26
Form a table with the probabilities in one column and the winnings in the next column
I'll also throw in a column to keep track of which event it corresponds to
| You selected... | Winnings | Probability | | A Face card | 500 | 3/13 | | An Ace | 1000 | 1/13 | | A Red card | 100 | 1/2 | | Any other card | 0 | 9/26 |
Now let's add in another column by multiplying each winning value with the corresponding probability
Eg: 500*(3/13) = 115.3846 approximately
| You selected... | Winnings | Probability | Winnings*Probability | | A Face Card | 500 | 3/13 | 115.3846 | | An Ace | 1000 | 1/13 | 76.9231 | | A Red Card | 100 | 1/2 | 50 | | Any Other Card | 0 | 9/26 | 0 |
The last step is to add the results of the final column:
115.3846 + 76.9231 + 50 + 0 = 242.3077
This rounds to 242.31
You should expect to win about $242.31
Answer: $242.31
|
|
|
