Question

Two players play each other in a pool tournament of "Solids and Stripes". The first player to win two games wins the tournament. In the game of "Solids and Stripes", it is equally likely that a player will be assigned solid balls or striped balls. Assume that 1) one-half of the balls are solids and the other half are stripes, 2) the two players have the same skill: each with a 0.5 probability of winning, 3) there are no ties, and 4) the tournament is concluded once a player has won two games. What is the expected number of games played in the tournament?

Answer #1

Let us say two players A and B are playing the game. Both of them have same chances of winning a game = 0.5

P( A wins ) = P( B wins) = 0.5

We consider 2 cases- a tournament with 2 games and a tournament with 3 games (in this case we will definitely have a winner)

P(tournament lasts 2 games) = (a particular player wins both the games) = 2 x 0.5 x 0.5 = 0.5

P(tournament lasts 3 games) = (a particular player wins 1 of first 2 games and 3rd game) = 2 x (2x0.5x0.5) x 0.5 = 0.5

Expected number of games = 2 x 0.5 + 3 x 0.5 = 1.5

There is a game with two players. Both players place $1 in the
pot to play. There are seven rounds and each round a fair coin is
flipped. If the coin is heads, Player 1 wins the round. Otherwise,
if it is tails, Player 2 wins the round. Whichever player wins four
rounds first gets the $2 in the pot.
After four rounds, Player 1 has won 3 rounds and Player 2 has
won 1 round, but they cannot finish...

In a tennis tournament, the final contest will be played between
two
players, Beto and Enrique. Betting names favor
Enrique in 1: 3 (this means that of 4 games made, it is
expected
May Beto win 1 and Enrique 3). The rule to define the end of
the
tournament championship is that games are played until a
winner. A winner will emerge when:
1. One of the two manages to accumulate three games won.
The winner will be the one...

A volleyball team is entered in a tournament. Rounds of the
tournament are played as best of three; that is, each team will
play the opponent in that round until one of the teams has won two
games.
Suppose that teams are matched up evenly in the first round of
the tournament, such that either team has an equal chance to win.
For subsequent games, if a team had just won they will be more
confident and more likely to...

Two players P1 and P2 agree to play the following game. Each
puts up a stake of 1 unit. They will play seven rounds, where each
round involves flipping a fair coin. If the coin comes up H, P1
wins the round, otherwise P2 wins. The first player to win four
rounds gets both stakes. After four rounds, P1 has won three rounds
and P2 has won one round, but they have to stop. What is the
fairest way to...

You enter a special kind of chess tournament, whereby you play
one game with each of three opponents, but you get to choose the
order in which you play your opponents. You win the tournament if
you win two games in a row. You know your probability of a win
against each of the three opponents. What is your probability of
winning the tournament, assuming that you choose the optimal order
of playing the opponents?

Write a program that allows two players to play a game of
tic-tac-toe. Use a twodimensional char array with three rows and
three columns as the game board. Each element in the array should
be initialized with an asterisk (*). The program should run a loop
that:
• Displays the contents of the board array.
• Allows player 1 to select a location on the board for an X.
The program should ask the user to enter the row and...

Two teams play a series of games until one of the teams wins n
games. In every game, both teams have equal chances of winning and
there are no draws. Compute the expected number of the games played
when (a) n = 2; (b) n = 3. (To keep track of what you are doing, it
can be easier to use different letters for the probabilities of win
for the two teams).

Markov Chains:
In baseball, basketball, tennis, and various other sports, the
winner of a tournament is determined by a best of five or best of
seven rule; that is, whichever team can win three or, respectively,
four games first is the winner of the series. Such tournaments are
presumed to be more fair than a single elimination game in
determining the better team, since the outcome of any single game
has a large element of chance. Suppose that two teams,...

A tennis player has two chances to get a serve into play. If the
first serve is out, the player serves again. If the second serve is
also out, the player loses a point. Here are the probabilities
based on four years of Wimbledon Championship: P(1st serve in) =
0.59, P(win a point|1st serve in) = 0.71, P(2nd serve in|1st serve
out) = 0.86, P(win a point|1st serve out and 2nd serve in) =
0.59.
a. Draw an accurate, properly...

Suppose that on each play of a certain game a gambler is equally
likely to win or to lose. Let R = Rich Rate. In the first game
(n=1), if a player wins, his fortune is doubled (r= 2), and when he
loses, his fortune is cut in half (r= 1/2).
a) For the second game (n = 2), R can take values r={4,1,1/4}
(Why?). Let i be the number of wins in n games. What are the
possible values...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 6 minutes ago

asked 14 minutes ago

asked 17 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago