You have in your pocket two coins, one bent (comes up heads with probability 3/4) and...
You have in your pocket two coins, one bent (comes up heads with probability 3/4) and one fair (comes up heads with probability 1/2). Not knowing which is which, you choose one at random and toss it. If it comes up heads you guess that it is the biased coin (reasoning that this is the more likely explanation of the observation), and otherwise you guess it is the fair coin.
A) What is the probability that your guess is wrong?
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You have in your pocket two coins, one bent (comes up heads with
probability 3/4) and...
Suppose there are two coins. One is a standard fair coin, so that P(heads)=0.50. The other...
Suppose there are two coins. One is a standard fair coin, so that P(heads)=0.50. The other one is a two-sided coin, so that P(heads)=1. You draw one of the two coins at random and toss it. It results in heads. Given that observation... (a) Compute the probability that you have selected a fair coin. (1pt) (b) What is the probability that the next toss will result in heads too? (1pt) (c) If the next toss results in heads as well,...
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.
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?
6 X Yos have seven coins in youe pocket coins Ceech with probsbility of "heads0.5o Pour two-heaed cons (each with probslity of heade1.0 Suppose you randomily select a coin and g it Find...
6 X Yos have seven coins in youe pocket coins Ceech with probsbility of "heads0.5o Pour two-heaed cons (each with probslity of heade1.0 Suppose you randomily select a coin and g it Find the probablity of lipping "bead Now suppose that you do, in fact, Bip "heads" Givea hat information, find the probabibty that the coin you aipped was: b. A fair con? sA two-headed coin? d. Now suppose that when you flip it, the coin comes up "tails". Given...
Suppose you have two coins. One coin is fair and other is a coin with heads...
Suppose you have two coins. One coin is fair and other is a coin with heads on both sides. Now you choose a coin at random and flip the coin. If the coin lands head, what is the probability that it was the fair coin?
You have five coins in your pocket. You know a priori that one coin gives heads with probability 0.4, and the other four coins give heads with probability 0.7 You pull out one of the five coins at ra...
You have five coins in your pocket. You know a priori that one coin gives heads with probability 0.4, and the other four coins give heads with probability 0.7 You pull out one of the five coins at random from your pocket (each coin has probability 릊 of being pulled out), and you want to find out which of the two types of coin it is. To that end, you flip the coin 6 times and record the results X1...
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?
there are two coins. One is fair and the other one has a 5/8 probability to...
there are two coins. One is fair and the other one has a 5/8 probability to heads. A coin is chosen at random and tossed twice. Heads shows twice. What is the probability the coin you chose is the biased one
(1 point) Consider a game played by flipping biased coins where the probability of heads is...
(1 point) Consider a game played by flipping biased coins where the probability of heads is 0.14. You first choose the number of coins you want to flip You must pay $1.5 for each coin you choose to flip. You flip all the coins at the same time. You win $1000 if one or more coins comes up heads How many coins should you flip to maximize your expected profit? Answer: What is your maximum expected profit? Answer: $ (Your...
Alice has two coins. The probability of Heads for the first coin is 1/4, and the...
Alice has two coins. The probability of Heads for the first coin is 1/4, and the probability of Heads for the second is 3/4. Other than this difference, the coins are indistinguishable. Alice chooses one of the coins at random and sends it to Bob. The random selection used by Alice to pick the coin to send to Bob is such that the first coin has a probability p of being selected. Assume that 0<p<1. Bob tries to guess which...
Suppose there are two coins. One is a standard fair coin, so that P(heads)=0.50. The other one is a two-sided coin, so that P(heads)=1. You draw one of the two coins at random and toss it. It results in heads. Given that observation... (a) Compute the probability that you have selected a fair coin. (1pt) (b) What is the probability that the next toss will result in heads too? (1pt) (c) If the next toss results in heads as well,...
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?
6 X Yos have seven coins in youe pocket coins Ceech with probsbility of "heads0.5o Pour two-heaed cons (each with probslity of heade1.0 Suppose you randomily select a coin and g it Find the probablity of lipping "bead Now suppose that you do, in fact, Bip "heads" Givea hat information, find the probabibty that the coin you aipped was: b. A fair con? sA two-headed coin? d. Now suppose that when you flip it, the coin comes up "tails". Given...
You have five coins in your pocket. You know a priori that one coin gives heads with probability 0.4, and the other four coins give heads with probability 0.7 You pull out one of the five coins at random from your pocket (each coin has probability 릊 of being pulled out), and you want to find out which of the two types of coin it is. To that end, you flip the coin 6 times and record the results X1...
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?
(1 point) Consider a game played by flipping biased coins where the probability of heads is 0.14. You first choose the number of coins you want to flip You must pay $1.5 for each coin you choose to flip. You flip all the coins at the same time. You win $1000 if one or more coins comes up heads How many coins should you flip to maximize your expected profit? Answer: What is your maximum expected profit? Answer: $ (Your...
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