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(a) A gambler has in his pocket a fair coin and a two-headed coin. He selects one of the coins at random, and when he flips it, it shows heads. What is the probability that it is the fair coin?
(b) Suppose that he flips the same coin a second time and again it shows heads. Now what is the probability that it is the fair coin?
(c) Suppose that he flips the same coin a third time and it shows tails. Now what is the probability that it is the fair coin?
new answer please not from old thank you (a) A gambler has in his pocket a...
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A gambler has in his pocket a fair coin and a two-headed coin. He selects one of the coins at random and flips it. What is the probability that the coin shows a head?
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...
Tom has three coins. Two are fair and one is unfair coin weighted so that heads is three times as likely as tails. He selects one of the coins at random and flips it. What is the probability it comes up heads? If it does come up heads, what is the probability it was the unfair coin?
Franklin has three coins, two fair coins (head on one side and tail on the other side) and one two-headed coin. 1) He randomly picks one, flips it and gets a head. What is the probability that the coin is a fair one? 2) He randomly picks one, flips it twice. Compute the probability that he gets two tails. 3) He randomly picks one and flips it twice. Suppose B stands for the event that the first result is head, and...
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...
Q.1 (25') Pony is playing coin tossing game with Yanny. They found the coin have 4 heads and 6 tails in 10 flips. Let p be the probability for obtaining a head, based on the first 10 flips a) Can we conclude it is a biased or fair coin base on the result above? b) Plot the Bernoulli's PMF What is the probability for obtaining 6 heads in 10 flips using the same coin? d) What is the probability for...
One gambler flips a fair coin in three separate times. Letting a random variable X represent his winnings in the following way: He loses $1 if he gets no heads in three flips; he wins $1, $2, and $3 if he obtains 1, 2, or 3 heads, respectively. (a) Find the probability mass function of X. (b) Find the probability density function of X. (c) Find the cumulative distribution function of X. (d) Find the probability that he wins more...
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...
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questions is a, b, c
Suppose that we have 3 coins. The coins are tossed, yielding the data in the following table: Coin 1 Coin 2 Coin 3 HEADS 29 23 42 TAILS 21 17 18 a. Test the null hypothesis that all 3 coin are fair. b. Test the null hypothesis that coin...