Question

In: Statistics and Probability

We have three cards. One is red on both sides; one is blue on both sides;...

We have three cards. One is red on both sides; one is blue on both sides; one is red on one side and blue on the other side. The cards are shuffled and their orientation randomized. One card is drawn and placed on the table; the side facing up is blue.

(a) Compute the information content of this observation (that the side facing up is blue.)

(b) Find the prior and posterior probability distributions of the color of the bottom side of the card. (Use Bayes’ theorem to calculate the posterior probability distributions.)

(c) Find the entropy of each of the probability distributions you calculated in part (a).

Expert Solution

Answer:-

Given That:-

We have three cards. One is red on both sides; one is blue on both sides; one is red on one side and blue on the other side. The cards are shuffled and their orientation randomized. One card is drawn and placed on the table; the side facing up is blue.

We have Three cards Among them

one is red on both sides.

one is blue on both sides

one is red on one side and blue on their side.

(a) Compute the information content of this observation (that the side facing up is blue.)?

The cards are shuffled ,One card is drawn and that is facing up to blue .

Here, there are 2 chances to get the card facing up is blue they are.

Either both sides blue (or) One side red and One side blue..

Total possibilities =3(i.e., one side is blue , both sides blue no blue.)

Avialiable possibilities = 2(i.e., 1 side blue , 2 sides blue)

Possibility

(b) Find the prior and posterior probability distributions of the color of the bottom side of the card. (Use Bayes’ theorem to calculate the posterior probability distributions.)?

To get the Prior and Posterios probability distribution of the color of the bottom side of the card .using Bayes' theorem as,

P(other side is blue \ side we see is blue)

(c) Find the entropy of each of the probability distributions you calculated in part (a).?

Entropy

orchestra answered 2 years ago

Six cards are identical except that both sides of two cards are red, both sides of three cards are black

Six cards are identical except that both sides of two cards are red, both sides of three cards are black, and the sixth card has one red side and one black side. One of the six cards is chosen at random and placed on a table. If the upper side of the chosen card is red, what is the probability that the bottom side is black?

Suppose we have 3 cards identical in form except that both sides of the first card...

Suppose we have 3 cards identical in form except that both sides of the first card are colord red, both sides of the second card are colored black and one side of the third card is colored red and the other side is black. The three cards are mixed up in a hat, and 1 card is randomly selected and put on the ground. If the upper side of the chosen card is colored red, what is the probability that...

Suppose that there are 8 blue credit cards, 6 red credit cards and 4 blue debit...

Suppose that there are 8 blue credit cards, 6 red credit cards and 4 blue debit cards in a box. It is known that color and card type are to be independent when a card is selected at random from this box. a) How many red debit cards must be present? b) Suppose that, 6 cards are randomly selected in a row with replacement. What is the probability that 2 blue credit cards and 2 blue debit cards are selected?...

Suppose that we have a red coin and a blue coin. The red coin has probability...

Suppose that we have a red coin and a blue coin. The red coin has probability pR = 0.1 of landing heads, and the blue coin has probability pB = 0.2 of landing heads. (a) Write R code to generate a sequence of coin tosses, starting with the red coin, and switching coins every time a coin lands heads. (b) Generate 1000 such sequences, each consisting of 1000 coin tosses, and use them to construct a plot of the 2.5%,...

A friend makes three pancakes for breakfast. One of the pancakes is burned on both sides,...

A friend makes three pancakes for breakfast. One of the pancakes is burned on both sides, one is burned on only one side, and the other is not burned on either side. You are served one of the pancakes at random, and the side facing you is burned. What is the probability that the other side is burned? (Hint: Use conditional probability.) Enter the exact answer. **The answer is NOT 0.5 or 1/2, when I put either of those, it...

Suppose that 8 cards, of which four are red, two are green and two are blue,...

Suppose that 8 cards, of which four are red, two are green and two are blue, are placed at random in 8 envelopes . Two envelops are selected at random, find the probability that the envelops have red cards? find the probability that they have cards of the same colors?

Suppose you have 24 items (three red, three blue, three yellow, and three green) to give...

Suppose you have 24 items (three red, three blue, three yellow, and three green) to give to 24 students. How many different ways can you distribute the things to the students? (Note: the items of the same color are identical)

We have a bag that contains n red balls and n blue balls. At each of...

We have a bag that contains n red balls and n blue balls. At each of 2n rounds we remove one of the balls from the bag randomly, and place it in one of available n bins. At each round, each one of the balls that remain in the bag is equally likely to be picked, as is each of the bins, independent of the results of previous rounds. Let Nk be the number of balls in the k-th bin...

Of 121 coins, one has a symbol on both sides, the others have a number on...

Of 121 coins, one has a symbol on both sides, the others have a number on one side and a symbol on the other. Otherwise the coins cannot be distinguish between them. After good mixing in a bag, one of the coins is pulled out and threw it three times in a row. After each throw there is a symbol on top. a)Then what is the probability that the coin with the two symbols was pulled? b)How many times had...

1. Suppose that you have ten cards. Five are red, three are yellow and two are...

1. Suppose that you have ten cards. Five are red, three are yellow and two are blue. The five red cards are numbered 1, 2, 3, 4, and 5. The three yellow cards are numbered 1, 2, and 3. The two blue cards are numbered 1 and 3. The cards are well shuffled. You randomly draw one card. Let R be the event that the card drawn is red and O be the event that the card drawn is odd-numbered....