Homework Answers
Both Alice and Bob have equal probability of winning game.
In a series of tosses, after a tail shows up, the next toss could show a head or a tail with equal probability of 1/2. So both tail-tail and tail-head sequences are equally probable to occur.
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Problem 2: Tails and (Heads or Tails?) Alice and Bob play a coin-tossing game. A fair...
Stacy and George are playing the heads or tails game with a fair coin. The coin is flipped repeat...
Stacy and George are playing the heads or tails game with a fair coin. The coin is flipped repeatedly until either the fifth heads or the fifth tails appears. If the fifth heads occurs first, Stacy wins the game. Otherwise, George is the winner. Suppose that after the fifth flip, three heads and two tails have occurred. What is the probability that Stacy wins this game?
This is discrete mathematics If you do it right, I must give praise. You must use probability spa...
This is discrete mathematics
If you do it right, I must give praise.
You must
use probability space is a triple relative
acknowledge.
S: is a
sample sapce
E=p(s) is
the set of all events
P:
E-->R is a function.
The important thing that I need to say three times:
If you don't know how to do it, please don't do
it.
don't copy others,
especially for question (a), give sample space, probability
measure
The important thing that I need...
Suppose you flip a fair coin repeatedly until you see a Heads followed by another Heads...
Suppose you flip a fair coin repeatedly until you see a Heads followed by another Heads or a Tails followed by another Tails (i.e. until you see the pattern HH or TT). (a)What is the expected number of flips you need to make? (b)Suppose you repeat the above with a weighted coin that has probability of landing Heads equal to p.Show that the expected number of flips you need is 2+p(1−p)/1−p(1−p)
71. A game involves selecting a card from a regular 52-card deck and tossing a coin....
71. A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails. • If the card is a face card, and the coin lands on Heads, you win $6 • If the card is a face card, and the coin lands on Tails, you win $2 • If the card is not a face card, you lose $2, no matter...
Suppose that a fair coin is tossed ten times. Each time it lands heads you win...
Suppose that a fair coin is tossed ten times. Each time it lands heads you win a dollar, and each time it lands tails you lose a dollar. Calculate the probability that your total winnings at the end of this game total two dollars, and the probability that your total winnings total negative two dollars.
4. A fair two-sided coin is tossed repeatedly. (a) Find the expected number of tails until...
4. A fair two-sided coin is tossed repeatedly. (a) Find the expected number of tails until the first head is flipped. (b) Find the probability that there are exactly 5 heads in the first 10 flips. (c) Use the central limit theorem/normal approximation to approximate the probability that in the first 100 flips, between 45 and 55 of the flips are heads.
A fair coin is tossed 6 times. A) What is the probability of tossing a tail...
A fair coin is tossed 6 times. A) What is the probability of tossing a tail on the 6th toss given the preceding 5 tosses were heads? B) What is the probability of getting either 6 heads or 6 tails?
Amanda, Becca, and Charise toss a coin in sequence until one person “wins” by tossing the...
Amanda, Becca, and Charise toss a coin in sequence until one person “wins” by tossing the first head. a) If the coin is fair, find the probability that Amanda wins. b) If the coin is fair, find the probability that Becca wins. c) If the coin is fair, find the probability that Charise wins. d) The coin is no longer fair. The probability that the coin comes up heads on an individual toss is p, for 0<p<1. Plot each players...
35. You and I play the following game: I toss a coin repeatedly. The coin is...
35. You and I play the following game: I toss a coin repeatedly. The coin is unfair and P(H) = p. The game ends the first time that two consecutive heads (HH) or two consec- utive tails (TT) are observed. I win if (HH) is observed and you win if (TT) is observed. Given that I won the game, find the probability that the first coin toss resulted in heads?
4. Alice and Bob take turns rolling a fair six sided die. They keep playing this...
4. Alice and Bob take turns rolling a fair six sided die. They keep playing this game until someone gets a 6, and that person is declared the winner. Alice goes first. Find the probability that Alice wins the game. Hint: The probability should be more than 0.5 Example of Alice winning in 5 turns: В А В А 2 2 6
This is discrete mathematics
If you do it right, I must give praise.
You must
use probability space is a triple relative
acknowledge.
S: is a
sample sapce
E=p(s) is
the set of all events
P:
E-->R is a function.
The important thing that I need to say three times:
If you don't know how to do it, please don't do
it.
don't copy others,
especially for question (a), give sample space, probability
measure
The important thing that I need...
Suppose that a fair coin is tossed ten times. Each time it lands heads you win a dollar, and each time it lands tails you lose a dollar. Calculate the probability that your total winnings at the end of this game total two dollars, and the probability that your total winnings total negative two dollars.
4. A fair two-sided coin is tossed repeatedly. (a) Find the expected number of tails until the first head is flipped. (b) Find the probability that there are exactly 5 heads in the first 10 flips. (c) Use the central limit theorem/normal approximation to approximate the probability that in the first 100 flips, between 45 and 55 of the flips are heads.
35. You and I play the following game: I toss a coin repeatedly. The coin is unfair and P(H) = p. The game ends the first time that two consecutive heads (HH) or two consec- utive tails (TT) are observed. I win if (HH) is observed and you win if (TT) is observed. Given that I won the game, find the probability that the first coin toss resulted in heads?
4. Alice and Bob take turns rolling a fair six sided die. They keep playing this game until someone gets a 6, and that person is declared the winner. Alice goes first. Find the probability that Alice wins the game. Hint: The probability should be more than 0.5 Example of Alice winning in 5 turns: В А В А 2 2 6
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