Question

In: Statistics and Probability

You are to play three games. In the first game, you draw a card, and you...

You are to play three games. In the first game, you draw a card, and you win if the card is a heart. In the second game, you toss two coins, and you win if one head and one tail are shown. In the third game, two dice are rolled and you win if the sum of the dice is 7 or 11. What is the probability that you win all three games? What is the probability that you win exactly two games?

Solve the question using Tree Diagram. Please give explanation for the answer.

Expert Solution

Probabilities of winning in each game

Game 1:

= Number of heart cards / Total number of cards in a deck = 13/52 = 0.25

Game 2:

= Probability of getting HT or TH in tossing two coins = 1/2 = 0.5

Game 3:

= Probability of getting the events {16, 25, 34, 43, 52, 56, 61, 65} in tossing two coins

= 8/36

= 0.2222

Hence, Probabilities of losing in each game are:

Now consider the Tree Diagram:

From the above tree diagram,

Probability of winning all Three Games = Probability of WWW = 0.0278

Probability of winning exactlly two games = Probability of WWL + Probability of WLW + Probability of LWW

= 0.0972 + 0.0278 + 0.0833

= 0.2083

Hence, the probability that you win all three games is 0.0278.

And, the probability that you win exactly two games is 0.2083.

orchestra answered 1 year ago

Play the following games in the Games Fair: Three Prize Roller Word Scramble Marble Draw Ten...

Play the following games in the Games Fair: Three Prize Roller Word Scramble Marble Draw Ten Spinner For each Games Fair game, answer the following questions: Create the probability distribution in a table for all the outcomes where X is the random variable representing the number of points awarded. Communicate how you arrived at the probability of each outcome. What is the expected value, E(X), for the game? You may include this in your table from the distribution. If the...

A card game at a casino costs $10 to play. One card is selected at random...

A card game at a casino costs $10 to play. One card is selected at random from a standard deck. If a heart is selected the player wins $19. If a spade is selected, the player wins $14. If a club or diamond is selected, the player wins nothing. What is the expected value of this game to the player? Round your answer to the nearest cent. Do not include the $ sign in your answer. A homeowner purchases an...

If you draw a card with a value of three or less from a standard deck...

If you draw a card with a value of three or less from a standard deck of cards, I will pay you $47. If not, you pay me $12. (Aces are considered the highest card in the deck.) ) Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values

Problem 5 (6 pts). A and B play a series of games. Each game is independently...

Problem 5 (6 pts). A and B play a series of games. Each game is independently won by A with probability p and by B with probability 1 − p. They stop when the total number of wins of one of the players is two greater than that of the other player. The player with the grater number of total wins is declared the winner of the series. Find the probability that a total of 4 games are played.

Question 7 (1 point) Poker game: You pay $5 to play. A 7-card poker hand is...

Question 7 (1 point) Poker game: You pay $5 to play. A 7-card poker hand is dealt, and you are paid $89 if the hand contains a 3 of a kind [at least 3 cards of the same value] and nothing otherwise. What is the expected value of your payoff from this game? [Round to 3 digits after decimal point] Your Answer:

IN C++ Write a program to play the Card Guessing Game. Your program must give the...

IN C++ Write a program to play the Card Guessing Game. Your program must give the user the following choices: - Guess only the face value of the card. -Guess only the suit of the card. -Guess both the face value and suit of the card. Before the start of the game, create a deck of cards. Before each guess, use the function random_shuffle to randomly shuffle the deck.

Teams A and B play in a basketball tournament. The first team to win two games...

Teams A and B play in a basketball tournament. The first team to win two games in a row or a total of three games wins the tournament. What is the number of ways the tournament can occur? 14 12 8 10 How many different rearrangements are there of the letters in the word BUBBLE? 60 100 120 80 How many ways are there to arrange all the words in this tongue twister? CAN YOU CAN A CAN AS A...

PYTHON: Write the code to play a card game called Battle. Two players each have a...

PYTHON: Write the code to play a card game called Battle. Two players each have a card deck consisting of the following cards: two, three, four, … jack, queen, king, ace, in increasing order. One card deck could be represented by a list such as: cardsPlayer1 = ["two", "three", "four"..."jack", "queen", "king", "ace"] Both players have a card randomly selected. When a card is selected, remove it from the player’s deck. The player that plays the higher of the two...

USING JAVA... We want to play a simple card game with 2 players option. The deck...

USING JAVA... We want to play a simple card game with 2 players option. The deck of cards contains 52 cards with 13 cards each in the 4 suits: clubs, diamonds, hearts and spades. Each player begins with 26 cards and one of the players starts the game by putting their ﬁrst card on the table. Players take turns by putting the top card from their hand, until the current card placed on the table matches the suit of the...

You draw a card from a deck. If you get a red card, you win nothing....

You draw a card from a deck. If you get a red card, you win nothing. If you get a spade, you win $5 . For any club, you win $10 plus an extra $25 for the ace of clubs. Find the standard deviation of the amount you might win drawing a card. The standard deviation is $nothing .