Rosencrantz and Guildenstern are flipping coins. Guildenstern has a bag with 100 coins in it. All...
Rosencrantz and Guildenstern are flipping coins. Guildenstern has a bag with 100 coins in it. All of them are fair coins, except for 10 that each have heads on both sides and 2 that each have tails on both sides. Guildenstern reaches into the bag without looking, removes a randomly chosen coin, with each of the 100 coins equally likely, and flips it. Give exact answers expressed as simplified fractions.
(a) What is the probability that it is one of the 2-headed coins, given that the flip came up heads?
(b) What is the probability that it is one of the fair coins, given that the flip came up heads?
(c) What is the probability that it is one of the fair coins, given that the flip came up tails?
Homework Answers
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Rosencrantz and Guildenstern are flipping coins. Guildenstern
has a bag with 100 coins in it. All...
4. Suppose that I flip a penny and a nickel, each coin is equally likely to...
4. Suppose that I flip a penny and a nickel, each coin is equally likely to come up heads and tails, and the two flips are independent Part a: What is the conditional probability that both coins come up heads, given that the penny came up heads? Part b: What is the conditional probability that both coins come up heads, given that (at least) one of the coins came up heads? Hint: The answers to the two parts here are...
There are two coins in a sack. They look and feel identical in every way, except...
There are two coins in a sack. They look and feel identical in every way, except that one is a regular coin with a head and tail side; the other is a 2 headed coin with a head on both sides. When the regular coin is flipped, H and T each show with probability .5. When the 2 headed coin is flipped, H shows with probability 1. Each coin is equally likely to be pulled out of the sack. A...
Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probability 0.5 and tails with probability 0.5) and one i...
Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probability 0.5 and tails with probability 0.5) and one is a trick coin which alwavs flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin. (a) What is the...
2. Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probabilty 0.5 and tails with probability 0.5) and one...
2. Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probabilty 0.5 and tails with probability 0.5) and one is a trick coin which always flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin (a) What is...
Problem 6 A box contains 4 coins: • coin 1 has both sides heads. • coin...
Problem 6 A box contains 4 coins: • coin 1 has both sides heads. • coin 2 has both sides tails. • coin 3 has both sides tails. • coin 4 is a regular coin (1 side head, other side tails). (a)(3 points) If we randomly choose one coin from the box and flip, what is the probability we get heads? (b)(3 points) If we randomly choose one coin, flip, and it comes up heads, what is the probability it...
a bag contains one fair coin, two two-headed coins, and three two-tailed coins. each of the...
a bag contains one fair coin, two two-headed coins, and three two-tailed coins. each of the is flipped, but the outcomes of the fice coins are hidden from you, randomly. if the outcome you see is headsm, what is the probability that the fair coin (which may or may not be the coin that was shown to you) panded heads up?
Problem 2 Suppose you flip a penny and a dime. Each coin is equally likely to...
Problem 2 Suppose you flip a penny and a dime. Each coin is equally likely to come up heads and tails. The two flips are independent a) What is the sample space? b) What is the conditional probability that both coins come up heads, given that the penny comes up heads? c) What is the conditional probability that both coins come up heads, given that at least one of the coins comes up heads? (Hint: the answers in part (b)...
magine flipping twelve fair coins. a. What is the theoretical probability that all twelve will come...
magine flipping twelve fair coins. a. What is the theoretical probability that all twelve will come up tails? b. What is the theoretical probability the first toss is heads AND the next eleven are tails? a. P(all twelve tosses are tails)equals StartFraction 1 Over 4096 EndFraction (Type an integer or a simplified fraction.) b. P(first toss is heads and next eleven tosses are tails)equals nothing (Type an integer or a simplified fraction.)
casino Carl loves flipping coins. In fact, he is preparing to flip a coin 50 times...
casino Carl loves flipping coins. In fact, he is preparing to
flip a coin 50 times and track how many heads he gets (from zero to
50)
Casino Carl loves flipping coins. In fact,he is preparing to flip a coin 50 times and track how many heads he gets (from zero to 50). Use the normal approximation to find the probability Carl gets 20 heads or less from his 50 flips? Select one: a. 0.1563 b. 0.1014 C.0.0986 d. 0.0793
You have 5 coins, four of which are fair coins, i.e. P(H)=P(T)= 0.5, and the other...
You have 5 coins, four of which are fair coins, i.e. P(H)=P(T)= 0.5, and the other of which is a two headed coin, i.e. both sides have a head. Suppose you select a coin at random and flip in 3 times, getting all heads. If you flip the coin again, what is the probability it will be heads?
4. Suppose that I flip a penny and a nickel, each coin is equally likely to come up heads and tails, and the two flips are independent Part a: What is the conditional probability that both coins come up heads, given that the penny came up heads? Part b: What is the conditional probability that both coins come up heads, given that (at least) one of the coins came up heads? Hint: The answers to the two parts here are...
Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probability 0.5 and tails with probability 0.5) and one is a trick coin which alwavs flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin. (a) What is the...
2. Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probabilty 0.5 and tails with probability 0.5) and one is a trick coin which always flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin (a) What is...
Problem 6 A box contains 4 coins: • coin 1 has both sides heads. • coin 2 has both sides tails. • coin 3 has both sides tails. • coin 4 is a regular coin (1 side head, other side tails). (a)(3 points) If we randomly choose one coin from the box and flip, what is the probability we get heads? (b)(3 points) If we randomly choose one coin, flip, and it comes up heads, what is the probability it...
Problem 2 Suppose you flip a penny and a dime. Each coin is equally likely to come up heads and tails. The two flips are independent a) What is the sample space? b) What is the conditional probability that both coins come up heads, given that the penny comes up heads? c) What is the conditional probability that both coins come up heads, given that at least one of the coins comes up heads? (Hint: the answers in part (b)...
casino Carl loves flipping coins. In fact, he is preparing to
flip a coin 50 times and track how many heads he gets (from zero to
50)
Casino Carl loves flipping coins. In fact,he is preparing to flip a coin 50 times and track how many heads he gets (from zero to 50). Use the normal approximation to find the probability Carl gets 20 heads or less from his 50 flips? Select one: a. 0.1563 b. 0.1014 C.0.0986 d. 0.0793
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