Question

Suppose that two teams play a series of games that ends when
one of them has won 3 games. Suppose that each game played is,
independently, won by team A with probability 7/10 . Let X be the number of games that are
played. |

(a) | Find P(X = 5) |

(b) | Find the expected number of games played. |

Answer #1

Suppose that two teams play a series of games that ends when
one of them has won 3 games. Suppose that each game played is,
independently, won by team A with probability
1/ 2 . Let X be the number of games that are
played.
(a)
Find P(X = 4)
(b)
Find the expected number of games played.

#5. Suppose that two teams (A and B) play a series of games that
ends when one of them has won 3 games. Suppose that each game
played is, independently, won by team A with probability p. Find
the probability distribution of number of games.

Suppose that two teams, A and B play a series of games that ends
when one of them has won 3 games. Suppose that games are played
independently and both teams have equal chances of winning in each
game. Let X be the number of games played.
(i) Find the probability mass function of X.
(ii) Find the expected value of X

Two teams A and B play a series of games until one team wins
four games. We assume that the games are played independently and
that the probability that A wins any game is p and B wins (1-p).
What is the probability that the series ends after...
a) 5 games
b) 6 games
c) 7 games
d) n games

Suppose that two teams are playing a series of games, each team
independently wins each game with 1/2 probability. The final winner
of the series is the first team to win four games. Let X be the
number of games that the two teams have played. Find the
distribution of X.

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).

Suppose that two teams (for fun, let’s call them the Domestic
Shorthairs and Cache Cows) play a
series of games to determine a winner. In a best-of-three series,
the games end as soon as one
team has won two games. In a best-of-five series, the games end as
soon as one team has won
three games, and so on. Assume that the Domestic Shorthair’s
probability of winning any one
game is p, where .5 < p < 1. (Notice that...

Two teams A and B play a series of at most five games. The first
team to win these games win the series. Assume that the outcomes of
the games are independent. Let p be the probability for team A to
win each game. Let x be the number of games needed for A to win.
Let the event Ak ={A wins on the kth trial}, k=3,4,5.
(a) What is P(A wins)?
Express the probability with p and k. Show...

In the baseball World Series, two teams play games until one
team has won four games; thus the total length of the series must
be between 4 and 7 games. What is the probability of having a World
Series with a length of 4 games under the assumption that the games
are independent events with each team equally likely to win?

In a baseball playoff series, the two teams are evenly matched.
The two teams must play until one team wins 4 games, and no ties
are possible. Use the rows of random numbers shown to approximate
the probability that the series will end in exactly 7 games

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 26 minutes ago

asked 46 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago