# Math

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 of the two coins he received by tossing it 3 times in a row and observing the outcome. Assume that for any particular coin, all tosses of that coin are independent.

Given that Bob observed k Heads out of the 3 tosses (where k=0,1,2,3), what is the conditional probability that he received the first coin?
Ans : 3^3-k*p/3^3-k*p+3^k*(1-p)
We define an error to have occurred if Bob decides that he received one coin from Alice, but he actually received the other coin. He decides that he received the first coin when the number of Heads, k, that he observes on the 3 tosses satisfies a certain condition. When one of the following conditions is used, Bob will minimize the probability of error. Choose the correct threshold condition.
Ans : k</= 3/2+1/2logp/1-p
For this part, assume that p=3/4.

What is the probability that Bob will guess the coin correctly using the decision rule from part 2?
Ans: 0.84375
Suppose instead that Bob tries to guess which coin he received without tossing it. He still guesses the coin in order to minimize the probability of error. What is the probability that Bob will guess the coin correctly under this scenario?
Ans : 0.75
Bob uses the decision rule of Part 2. If p is small, then Bob will always decide in favor of the second coin, ignoring the results of the three tosses. The range of such p's is [0,t). Find t.
Ans : 0.03571

1. 👍 13
2. 👎 2
3. 👁 294,350
1. Thanks, Friend. (Y)

1. 👍 0
2. 👎 5
2. How do you get the probability that Bob will guess the coin correctly without tossing?

1. 👍 0
2. 👎 5
3. 294,226 veiws on this question...wow..

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Math: Probablity

A penny, a nickel, and a dime are flipped at the same time. Each coin can come out either heads (H) or tails (T). a. What name is given to the act of flipping the coins? b. There are eight elements in the sample space (i.e.,

asked by Anonymous on February 15, 2014
2. ### Math

Luis has a coin that is weighted so that the probability that Heads appears when it is tossed is 0.55. Suppose that the coin is tossed 3 times. What is the probability that all 3 tosses are Heads? please help ,e to solve this

asked by sajid on February 17, 2012
3. ### Math

10. A coin is loaded so that the probability of heads is 0.55 and the probability of tails is 0.45, Suppose the coin is tossed twice and the results of tosses are independent. a.What is the probability of obtaining exactly two

asked by Renee on March 2, 2014
4. ### Math

Darrin tosses a quarter and a penny 20 times. He gets heads on both coins twice. Compare the theoretical probability of getting heads on both coins with Darrin’s experimental probability of getting heads on both coins. Why might

asked by Anonymous on April 25, 2017
5. ### Stat.

A trick coin has been weighted so that heads occurs with a probability of p  2 3, and p(tails)  1 3. If you toss this coin 72 times, a. How many heads would you expect to get on average? b. What is the probability of getting

asked by Nickie on January 27, 2013
1. ### Probability

A defective coin minting machine produces coins whose probability of Heads is a random variable Q with PDF fQ(q)={3q2,0,if q∈[0,1],otherwise. A coin produced by this machine is tossed repeatedly, with successive tosses assumed

asked by A on April 2, 2014
2. ### Maths

The probability of a biased coin landing on heads is 0.6. I flip the coin 150 times, how many times would the coin land on heads?

asked by Anonymous on September 8, 2016
3. ### Algebra Probability

A coin is tossed twice. What is the probability of tossing heads, and then tails, given that the coin has already shown heads in the first toss?

asked by Algebra Probability on March 18, 2018
4. ### Math

A biased coin lands heads with probabilty 2/3. The coin is tossed 3 times a) Given that there was at least one head in the three tosses, what is the probability that there were at least two heads? b) use your answer in a) to find

asked by Steve on June 10, 2018
5. ### probability

Tossing a pair of coins We have a white coin, for which P(Heads)=0.4 and a black coin for which P(Heads)=0.6. The flips of the same or of different coins are independent. For each of the following situations, determine whether the

asked by RVE on April 11, 2015