A 5-card hand is dealt from a standard 52-card deck. If the 5-card hand contains at least one ace, you win $11; otherwise, you lose $1. What is the expected value of the game? dollars. The expected value of the game is (Type an integer or a decimal rounded to two decimal places.)

A 5-card hand is dealt from a standard 52-card deck. If the 5-card hand contains at least one ace, you win $11; otherwise, you lose $1. What is the expected value of the game? dollars. The expected value of the game is (Type an integer or a decimal rounded to two decimal places.)

Name: A 5-card hand is dealt from a standard 52-card deck. If the 5-card ha
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: A 5-card hand is dealt from a standard 52-card deck. If the 5-card hand contains at least one ace, you win $11; otherwise, you lose $1.What is the expected value of the game?dollars.The expected value of the game is(Type an integer or a decimal roun

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: When playing roulette at a casino, a gambler is trying to decide whether to bet $5 on the number 13…

A: E(number 13 bet) = -0.26 cents P($20 profit) = 3/38 P($5loss) = 35/38

Q: Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is…

Q: A carnival game has prizes and probabilities as shown in the table below. How much should the game…

A: Introduction In this question we have to find the cost of game if the owner of the game wants to…

Q: When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 11…

A: Given Information: The bet amount for number 11= $15 Bet amount for 00,0,1 =$15 The expected value…

Q: When playing roulette at a casino, a gambler is trying to decide whether to bet $10 on the number 13…

A: From the provided information,For the $10 bet that the outcome is 00, 0, 1, 2, or 3, there is a…

Q: A bag contains 2 gold marbles, 7 silver marbles, and 26 black marbles. Someone offers to play this…

A: Here we have given the information, A bag contains 2 gold marbles, 7 silver marbles, and 26 black…

Q: A bag contains 2 gold marbles, 7 silver marbles, and 20 black marbles. Someone offers to play this…

A: To find: What is your expected value if you play this game?

Q: Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is…

A: In a standard deck of playing cards there are total 52 cards and 4 suits, such as hearts, diamonds,…

Q: A bag contains 1 gold marbles, 10 silver marbles, and 28 black marbles. Someone offers to play this…

A: It is given that Gold marbles = 1 Silver marbles = 10 Black marbles = 28 Total marbles = 39

Q: Suppose a game is played with one six-sided dice. If the dice is rolled and lands on 1, 2, or 3, the…

A: It is given that a game is played with one six-sided dice.

Q: ou are to draw one card from a deck. If it is an ace, you win $10; if it is a face card, youwin $1;…

A: You are to draw a card from a deck of 52 cards. If it is an ace, you win $10 If it is a face card,…

Q: A person randomly selects one of six envelopes. Each envelope contains a check that the person gets…

Q: A bag contains 2 gold marbles, 9 silver marbles, and 28 black marbles. Someone offers to play this…

A: Obtain the expected value of the game. The expected value of the game is obtained below as…

Q: A game-show spinner has these odds of stopping on particular dollar values: 55% for $5, 20% for…

A: The odds of player wining $500 is 15% and the odds of player wining $1,000 is 10%.

Q: Consider a game in which a fair die is rolled. If the die comes up 1, the player wins $4. If the die…

A: Expected amount is mean of the distribution So we need to create a probability distribution table…

Q: A bag contains 2 gold marbles, 7 silver marbles, and 23 black marbles. Someone offers to play this…

A: Given information- We have given that a bag contains 2 gold marbles, 7 silver marbles, and 23 black…

Q: A game-show spinner has these odds of stopping on particular dollar values: 45% for $5, 25% for $50,…

A: The mutually exclusive events are those which can not occur simultaneously. For example getting head…

Q: bag contains 2 gold marbles, 9 silver marbles, and 26 black marbles. Someone offers to play this…

Q: A bag contains 1 gold marbles, 9 silver marbles, and 21 black marbles. Someone offers to play this…

Q: You decide to spend some money and place a bet on the 2023 NFL Super Bowl. If the Philadelphia…

Q: In the game of craps, two dice are tossed. One of the many bets available is the “Hard-way 8.” A $1…

A: In this case, P(Getting two four on the same roll)=16×16=136 That is,…

Q: Deshaun has a deck of 10 cards numbered 1 through 10. He is playing a game of chance. This game is…

A: Given Favorable outcome =1 Total outcome=10 Loses $3.40

Q: When playing roulette at a casino, a gambler is trying to decide whether to bet $10 on the number 32…

A: Given information- We have given the probability of making $60 profit for the $10 bet that the…

Q: A bag contains 3 gold marbles, 10 silver marbles, and 23 black marbles. Someone offers to play this…

A: We are given: 3 gold marbles, 10 silver marbles, and 23 black marbles. Total number of…

Q: A bag contains 2 gold marbles, 9 silver marbles, and 21 black marbles. Someone offers to play this…

A: It is given that a bag contains 2 gold marbles, 9 silver marbles and 21 black marbles.When the gold…

Q: 5 t for a single number is - $1.06. For the $10 bet that the outcome is 00, 0, 1, 2, or 3, there is…

A: From the provided information,For the $10 bet that the outcome is 00, 0, 1, 2, or 3, there is a…

Q: When playing roulette at a casino, a gambler is trying to decide whether to bet $20 on the number 13…

A: We have given that Probability of making a net profit $100 is 5/38 Probability of losing $20 is…

Q: Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is…

A: We have given that two cards are drawn at random without replacement from a standard deck. P (Both…

Q: Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is…

Q: A bag contains 1 gold marbles, 6 silver marbles, and 21 black marbles. Someone offers to play this…

A: We have given that a bag contains 1 gold marbles, 6 silver marbles, and 21 black marbles.Total…

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

A 5-card hand is dealt from a standard 52-card deck. If the 5-card hand contains at least one ace, you win $11; otherwise, you lose $1.
What is the expected value of the game?
dollars.
The expected value of the game is
(Type an integer or a decimal rounded to two decimal places.)

Expert Solution

Step 1

In a deck of 52 cards we have 4 ace cards.

The probability of no ace card is computed as,

$P (N o a c e c a r d) = \frac{{}^{48}C_{5}}{{}^{52}C_{5}} = \frac{\frac{48!}{43! \times 5!}}{\frac{52!}{47! \times 5!}} = 0.658842$

Thus,

P(at least one ace card) = 1- P(No ace card)

= 1-0.658842

= 0.341158.

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

A bag contains 2 gold marbles, 9 silver marbles, and 20 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?
One option in a roulette game is to bet $20 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $20 you paid to play the game and you are awarded $20. If the ball lands elsewhere, you are awarded nothing and the $20 that you bet is collected. Find the expected payback for this roulette game if you bet $20 on red. The expected payback is $ (Round to the nearest cent as needed.)
Salma has a deck of 10 cards numbered 1 through 10. She is playing a game of chance. This game is this: Salma chooses one card from the deck at random. She wins an amount of money equal to the value of the card if an even numbered card is drawn. She loses $3.50 if an odd numbered card is drawn. (a) Find the expected value of playing the game. dollars (b) What can Salma expect in the long run, after playing the game many times? (She replaces the card in the deck each time.) Salma can expect to gain money. She can expect to win dollars per draw. Salma can expect to lose money. She can expect to lose dollars per draw. Salma can expect to break even (neither gain nor lose money). E E
When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 25 or to bet $15 that the outcome is any one of the five possibilities 00, 0, 1, 2, or 3. The gambler knows that the expected value of the $15 bet for a single number is - $1.58. For the $15 bet that the outcome 5 is 00, 0, 1, 2, or 3, there is a probability of 38 33 of making a net profit of $75 and a 38 probability of losing $15. a. Find the expected value for the $15 bet that the outcome is 00, 0, 1, 2, or 3. b. Which bet is better: a $15 bet on the number 25 or a $15 bet that the outcome is any one of the numbers 00, 0, 1, 2, or 3? Why? a. The expected value is $. (Round to the nearest cent as needed.) b. Since the expected value of the bet on the number 25 is V than the expected value for the bet that the outcome is 00, 0, 1, 2, or 3, the bet on is better.
Solve the problem that involves computing expected values in a game of chance. A numbers game run by many state governments allows a player to select a three-digit number from 000 to 999. There are 1000 such numbers. A bet of $14 is placed on a number. If the number is selected, the player wins $1,400. If any other number is selected, the player wins nothing. Find the expected value for the game. A. $12.60 OB. $1.40 OC. -$12.60 OD. -$1.40
A bag contains 5 gold marbles, 7 silver marbles, and 23 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $4, if it is silver, you win $3. If it costs $1 to play, what is your expected profit or loss if you play this game? $ Submit Question
A game is played using a standard 52-card deck. The player pays $3.00 to play and gets to pick one card at random from the deck. If the player picks an ace, they win $12.00. If they pick a face card, they win $7.00. If the player picks a numbered card, they win $1.00. What is the expected value of the game?
In the game of roulette, one of the simplest bets is to wager on red. Here if you bet $1 and the ball lands on a red number in the wheel, then you will win $2 (i.e. profit $1). If the ball lands on a black or green space in the wheel, then you win nothing. What is the expected value on this bet? See the wheel below and show the work that you did to complete this problem. No work = no credit.
A person randomly selects one of four envelopes. Each envelope contains a check that the person gets to keep. However, before the person can select an envelope, he or she must pay $15 to play. Determine the person's expectation if the checks in the envelopes are for $0, $3, $6, and $18. The expected value is $. (Simplify your answer. Type an integer or a decimal.)
When playing roulette at a casino, a gambler is trying to decide whether to bet $15 on the number 23 or to bet $15 that the outcome is any one of the three possibilities 00, 0 , or 100, 0, or 1. The gambler knows that the expected value of the $15 bet for a single number is -0.79 cents−0.79¢.For the $15 bet that the outcome is 00, 0 , or 100, 0, or 1,there is a probability of 3/38 of making a net profit of$60 and a 35/38 probability of losing $15 a. Find the expected value for the $15bet that the outcome is 00 , 0 ,or 100, 0, or 1. b. Which bet is better: a $15 bet on the number 23 or a $15 bet that the outcome is any one of the numbers 00 ,0 ,or 100, 0, or 1? Why?
An exclusive raffle is being held where only 7 tickets are available. The raffle is free to enter. If you choose to play, you could win $7 or lose $3. Three tickets are winning tickets and you will win $7 if your ticket is drawn. Four tickets are losing tickets where you must pay $3 if your ticket is drawn. What is the expected return if you enter the raffle?