A jar contains 100 coins, where 99 are fair, but one is double-headed (always landing heads)....
A jar contains 100 coins, where 99 are fair, but one is double-headed (always landing heads). A coin is chosen randomly from the jar. Then, the chosen coin is flipped 5 times.
(a) Compute the probability that the coin lands heads all 5 times.
(b) Given the coin lands heads all 5 times, what is the probability that the chosen coin is double-headed?
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A jar contains 100 coins, where 99 are fair, but one is
double-headed (always landing heads)....
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?
Question 4 (20 points) A box contains three coins, two fair coins and one two-headed coin....
Question 4 (20 points) A box contains three coins, two fair coins and one two-headed coin. (a) You pick a coin at random and toss it. What is the probability that it lands heads up? (b) You pick a coin at random and toss it, and get heads. What is the probability that it is the two-headed coin?
5.) A jar contains 50 type 1 coins and 50 type 2 coins. Type 1 coins...
5.) A jar contains 50 type 1 coins and 50 type 2 coins. Type 1 coins have probability 2/3 of landing on heads, while type 2 coins have probability 1/3 of landing on heads. If a coin is chosen at random from the jar and tossed 3 times, what is the probability that it lands on heads at least 2 times? 6) Suppose that an HIV-1 test has a false positive rate of 0.1% and a false negative rate of...
A box contains four coins. Three of the coins are fair, but one of them is...
A box contains four coins. Three of the coins are fair, but one of them is biased, with P(11) = ? (where 11 is the event of flipping heads). You take a coin from the box and flip it. It comes up heads. What is the probability that you have flipped the biased coin?
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...
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...
when coin 2 is flipped it lands on heads with When coin 1 is flipped, it...
when coin 2 is flipped it lands on heads with When coin 1 is flipped, it lands on heads with probability probability (a) If coin 1 is flipped 12 times, find the probability that it lands on heads at least 10 times. (b) If one of the coins is randomly selected and flipped 9 times, what is the probability that it lands on heads exactly 6 times? (c) In part (b), given that the first of these 9 flips lands...
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...
You have 2 fair coins and one coin with heads on both sides. You pick a...
You have 2 fair coins and one coin with heads on both sides. You pick a coin at random and toss it twice. If it lands heads up on both tosses, the probability it also lands heads up on a third toss can be express in the form A/B, where A and B are relatively prime positive integers (i.e. the greatest common divisor is 1). Compute A + B.
There are three coins. They have chances 0.4, 0.6 and 0.8 respectively of showing heads. One...
There are three coins. They have chances 0.4, 0.6 and 0.8 respectively of showing heads. One of these three coins is chosen at random and flipped. (a) What is the chance that the coin chosen is the coin with probability equal to .4 of showing heads and a head shows up after the flip? (b) What is the chance that the coin, when flipped, shows a head? (c) Given that the coin, when flipped, shows a head, what is the...
Question 4 (20 points) A box contains three coins, two fair coins and one two-headed coin. (a) You pick a coin at random and toss it. What is the probability that it lands heads up? (b) You pick a coin at random and toss it, and get heads. What is the probability that it is the two-headed coin?
5.) A jar contains 50 type 1 coins and 50 type 2 coins. Type 1 coins have probability 2/3 of landing on heads, while type 2 coins have probability 1/3 of landing on heads. If a coin is chosen at random from the jar and tossed 3 times, what is the probability that it lands on heads at least 2 times? 6) Suppose that an HIV-1 test has a false positive rate of 0.1% and a false negative rate of...
A box contains four coins. Three of the coins are fair, but one of them is biased, with P(11) = ? (where 11 is the event of flipping heads). You take a coin from the box and flip it. It comes up heads. What is the probability that you have flipped the biased coin?
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...
when coin 2 is flipped it lands on heads with When coin 1 is flipped, it lands on heads with probability probability (a) If coin 1 is flipped 12 times, find the probability that it lands on heads at least 10 times. (b) If one of the coins is randomly selected and flipped 9 times, what is the probability that it lands on heads exactly 6 times? (c) In part (b), given that the first of these 9 flips lands...
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...
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