a) Michael and Christine play a game where Michael selects a
number from the set {1,2,3,4,....8}....
a) Michael and Christine play a game where Michael selects a
number from the set {1,2,3,4,....8}. He receives N dollars if the
card selected is even; otherwise, Michael pays Christine two
dollars. Determine the value of N if the game is to be fair.
b) A biased coin lands heads with probability 1/4 . The coin is
flipped until either heads or tails has occurred two times in a
row. Find the expected number of flips.
Q1) Draw 4 chips one-by-one without replacement from an urn that
contains 14 red and 6...
Q1) Draw 4 chips one-by-one without replacement from an urn that
contains 14 red and 6 black chips. Suppose you win $5 for each
black chip drawn. Find your expected winnings.
Q2) Michael and Christine play a game where Michael selects a
number from the set {1,2,3,4,....8}. He receives N dollars if the
card selected is even; otherwise, Michael pays Christine two
dollars. Determine the value of N if the game is to be fair.
You are trying to decide whether to play a carnival game that
costs $1.50 to play....
You are trying to decide whether to play a carnival game that
costs $1.50 to play. The game consists of rolling 3 fair dice. If
the number 1 comes up at all, you get your money back, and get $1
for each time it comes up. So for example if it came up twice, your
profit would be $2. The table below gives the probability of each
value for the random variable X, where:
X = profit from playing the...
The game requires $5 to play, once the player is admitted, he
or she has the...
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
wins they may roll a dice for a second turn, if the die rolls on a
even number, they may pick from the bag once again with no extra...
In the “divide two apples” game, player 1 suggests a division
scheme (x,y) from the set...
In the “divide two apples” game, player 1 suggests a division
scheme (x,y) from the set {(2, 0), (1, 1), (0, 2)} where x is the
number of apples allocated to player 1, and y is the number of
apples allocated to player 2. Player 2 counters with a division
scheme of her own that comes from the same set. The final
allocation is obtained by averaging the two proposed division
schemes. The apples can be cut if the resulting...
Suppose you are playing a game of five-card poker where you are
dealt a hand of...
Suppose you are playing a game of five-card poker where you are
dealt a hand of 5 cards from a standard deck of 52 playing cards.
Each card has one of 13 values, 2,3,…,10,J,Q,K,A2,3,…,10,J,Q,K,A,
and one of 4 suits, ♡,♢,♠,♣♡,♢,♠,♣
A hand called a royal flush consists of cards of
the values 10,J,Q,K,A10,J,Q,K,A, all from the same suit. For
instance, a royal flush with hearts would be
10♡,J♡,Q♡,K♡,A♡10♡,J♡,Q♡,K♡,A♡.
Now, actually getting a royal flush in poker is incredibly rare (in...
Read this case study and then answer the questions that follow.
(The paragraphs are number 1...
Read this case study and then answer the questions that follow.
(The paragraphs are number 1 to 13 for your convenience).
1. Mr Michael Maguire lives in Wombat, in the central west
of New South Wales. Michael owns a 3000 acre farm in Young, and the
main crop he grows is cherries. He has decided he needs to acquire
a better and more efficient spraying machine.
2. Some specialist spraying machines are available in
Toronto, Canada at the firm Maple...