Asked by Rosa M. Martinez on May 07, 2024
Verified
You pick a card from a deck.If you get a face card,you win $15.If you get an ace,you win $30 plus an extra $60 for the ace of hearts.For any other card you win nothing.Find the expected amount you will win.
A) $8.08
B) $4.62
C) $6.92
D) $6.35
E) $7.50
Expected Amount
The predicted value or mean of all possible outcomes of a variable, weighted by their probabilities.
Probability Model
A mathematical representation of a random process, describing all possible outcomes and their associated probabilities.
Ace Of Hearts
A playing card in the heart suit, regarded as either the highest or lowest depending on the game.
- Utilize the concept of expected value across various situations.
- Determine the expected value of discrete random variables.
Verified Answer
The probability of getting a face card is 12/52 (since there are 12 face cards in a deck of 52 cards).
The probability of getting an ace is 4/52 (since there are 4 aces in a deck of 52 cards).
Therefore, the probability of winning nothing is 36/52.
So, the expected winnings are:
E(win) = (12/52) * $15 + (4/52) * ($30+$60) + (36/52) * $0
E(win) = $1.15 + $1.15 + $0
E(win) = $2.30
Therefore, the best choice is C, since it has the closest value to the expected winnings.
Learning Objectives
- Utilize the concept of expected value across various situations.
- Determine the expected value of discrete random variables.
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