Question: Suppose that a box contains five coins and that for each coin there is a different probability that a head will be obtained when the

Suppose that a box contains five coins and that for each coin there is a different probability that a head will be obtained when the coin is tossed. Let pi denote the probability of a head when the ith coin is tossed (i = 1, . . . , 5), and suppose that p = 0, p2 = 1/4, p3 = 1/2, p4 = 3/4, and p5 = 1.
a. Suppose that one coin is selected at random from the box and when it is tossed once, a head is obtained. What is the posterior probability that the ith coin was selected (i = 1, . . . , 5)?
b. If the same coin were tossed again, what would be the probability of obtaining another head?
c. If a tail had been obtained on the first toss of the selected coin and the same coin were tossed again, what would be the probability of obtaining a head on the second toss?

Step by Step Solution

★★★★★

3.44 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Let i denote the posterior probability that coin i was selected The prior probabi... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

602-M-S-P (5211).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Suppose that a box contains five red balls and ten blue balls. If seven balls are selected at random without replacement, what is the probability that at least three red balls will be obtained?

Suppose that a box contains r red balls and w white balls. Suppose also that balls are drawn from the box one at a time, at random, without replacement. (a) What is the probability that all r red...

Suppose that a box contains one blue card and four red cards, which are labeled A, B, C, and D. Suppose also that two of these five cards are selected at random, without replacement. a. If it is...

please answer all attentionfor the first question,0 COMPUTER SCIENCE complete the grading students' function below the function is expected to return an INTEGER ARRAY the function accepts...

A box contains four coins and for each coin there is a different probability that a head will be obtained when the coin is tossed. Let p, denote the probability of getting a head when the ith coin is...

A box contains 4 coins. Coin 1 is biased such that it comes up heads with probability 0.3. Coin 2 is fair, and equally likely to come up heads or tails. Coin 3 is biased such that it comes up heads...

(Updaing posterior probabilities. ) Recall the setting of problem 1 form homework 3. Suppose that a box contains a fair coin and a coin with a head on each side. Suppose also that one coin is...

1. Given P(A U B) = 0.9, P(An B) = 0.3, and P(A) = 0.5, find P(A | B) and P(B | A). 2. When a fair die is rolled five times, what is the probability that it comes up six exactly three times, given...

GIVE CORRECT ANSWERS AND STEPWISE CALCULATIONS 1) The lines L1 : 3x + 4y + 4 = 0 and L2 : 5x + 12y + 28 = 0 cut the x-axis at points A and B respectively. (a) Find the coordinates of A and B. (b) The...

A) If you assume the distribution of income is normally distributed, with mean 45,000 and standard deviation 15,000, what is the family income cutoff (the largest amount of family income that would...

Nature's Best Publishing Company pays its employees monthly. Payments made by the company on October 31, 2016, follow. Cumulative amounts paid to the persons named prior to October 31 are also given....

1. Prepare a presentation that describes current legal provisions that address the problem of unsolicited telephone calls, mailings, and email. Make recommendations for enforcement of existing laws...

If a 2 D array has 4 rows and 5 columns, which of the following represents the total number of elements in matrix? q , Cannot be determined 4 0 9 2 0

For which situation (centralization or decentralization) does risk pooling result in less safety stock? Why?

The number of cracks in a ceramic tile has a Poisson distribution with a mean of = 2.4. What is the probability that a tile has no cracks? What is the probability that a tile has four or more cracks?

On average there are about 25 imperfections in 100 meters of optical cable. Use the Poisson distribution to estimate the probability that there are no imperfections in 1 meter of cable. What is the...

On average there are four traffic accidents in a city during one hour of rush-hour traffic. Use the Poisson distribution to calculate the probability that in one such hour there arc (a) No accidents...

_ After COVE-19, the Clayton campus has turned into a postapocalyptic corrupt world where lecturers and students have to gamble to stay alive. Clayton campus has become Clayton lCasino. You attend...

How much would $10,000 due in 100 years be worth today if the discount rate were 10%? A. $0.73 B. $1.21 D. $4.83 E. $6.30 You have saved $5,000 for a down payment on a new car. The largest monthly...

1) A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows Full data set the results for the number of bacteria per cubic foot for both types...