Question

John and Kate play a game in which they take turns to toss a pair of dice. Whoever gets a total of 7 wins the game. If John tosses first and Kate tosses second, find the probability that:

a) John will win the game?

b) Kate will win the game?

Answer #1

Alice and Bob play the following game. They toss 5 fair coins.
If all tosses are Heads,Bob wins. If the number of Heads tosses is
zero or one, Alice wins. Otherwise they repeat,tossing five coins
on each round, until the game is decided. (a) Compute the
expectednumber of coin tosses needed to decide the game. (b)
Compute the probability that Alicewins.

Players A and B take turns at rolling two dice, starting with A.
The first person to get a sum of at least 9 on a roll of the two
dice wins the game.
Find the probability that A will win the game if:
(a) the game is just about to begin
(b) 8, 4, 3, 7 and 7 have already been rolled
(c) a draw is to be declared in the event of no-one winning
within 6 rolls.

Players A and B take turns at rolling two dice, starting with A.
The first person to get a sum of at least 9 on a roll of the two
dice wins the game. Find the probability that A will win the game
if:
(a) the game is just about to begin
(b) 8, 4, 3, 7 and 7 have already been rolled
(c) a draw is to be declared in the event of no-one winning
within 6 rolls.

Two brothers, Max and Sam, take turns at trying to win a prize.
Max, being the younger, goes first, and Sam goes second. If no one
wins on their first attempt, this process is repeated until someone
wins. For Max to win, he must roll a die for a 5 or a 6. For Sam to
win, he must toss a coin heads. What is the probability that Max
wins?

Three college students play a game every Thursday night. Only
one student can win the game. Based on past games, the probability
that the first student wins the game is 0.3 and the probability
that the second student wins the game is also 0.3. What is the
probability that the third student wins the game?

you are thinking of playing a game with a pair of dice. you will
win if the sum of the top faces is either 7 or 8. the loser pays
the winner $1 each game. should you play? set up a probability
distribution table and use it to find your expected earnings. Then
make your decisions.

Three players (Tom, jery and Harry) are playing the following
game: Starting with Tom, they take turns (in that particular order)
to roll a special die that has ‘3’ marked on three of its sides,
‘2’ marked on two of its sides and ‘1’ on the remaining side.
Whoever gets a ‘1’ for the first time wins the game. Find P(Tom
wins), P(jery wins) and P(Harry wins). If it is given that Harry
has won, what are the conditional chances...

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...

The game requires $5 to play, once the player is admitted, he
or she has the opportunity to take a chance with luck and pick from
the bag. If the player receives a M&M, the player loses. If the
player wins a Reese’s Pieces candy, the player wins. If the player
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Ahmed plays a game where he tosses two balanced 4
sided-dice, each with faces labeled by 1, 2, 3 and 4. He wins 2
points if the sum is 4. He wins 1 point if the sum is greater than
4. He loses k points if the sum is less than 4.
i. Find the probability distribution sum.
ii. Find the value of k which achieves the fairness of
game. (i.e. The fairness is achieved if the game is not...

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