There are two boxes containing only black and yellow pens. Box A has 5 yellow pens...
We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box number 2 contains two black and one white ball. Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one ball from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white. We are going to find MAP estimate for the...
Problem 2. We have 2 boxes, each containing 3 balls. Box number 1 contains one black and two white balls; box nber 2 contains two black and one white ba Our friend chooses one of the boxes at random, probability of choosing box number 1 is p. Then he takes one bal from a chosen box (each of three balls can be taken chosen equally likely), and it turns out to be white We are going to find MAP estimate...
5. Two identical boxes have chips in them. Box I has 4 blue chips and 2 red chips. Box II has 2 blue chips and 6 red chips. A box is randomly selected, and one chip is randomly drawn. a) What is the probability of drawing a red chip? b) Given that Box I was chosen, what is the probability of drawing a red chip? c) Based on your answers in parts a & b, are the events “drawing 1...
Two identical boxes have chips in them. Box I has 4 blue chips and 2 red chips. Box II has 2 blue chips and 6 red chips. A box is randomly selected, and one chip is randomly drawn. a) What is the probability of drawing a red chip? b) Given that Box I was chosen, what is the probability of drawing a red chip? c) Based on your answers in parts a & b, are the events “drawing 1 red...
Two marbles are chosen without replacement from a box containing 5 green, 8 red, 5 yellow, and 7 blue marbles. Let X be the number of red marbles chosen. a) Find and graph the probability distribution of X. b) Find E (x)
This question is about the Bayes' Theorem. You are given two boxes. Box 1 contains 5 red, 5 green, and 3 blue balls, and Box 2 contains 4 red, 3 green, and 2 yellow balls. You are asked to randomly pick one of the two boxes. Holding that box, you grab one ball at random, and then set the box back down. You found out that it is a red ball. Let A be the event that you choose Box...
Questi A marble is drawn from a box containing 5 yellow, 3 white, and 17 blue marbles. Find the odds in favor of drawing the following. (a) A yellow marble (b) A blue marble (c) A white marble (d) Not drawing a white marble Questi Questi (a) In reduced form, the odds in favor of drawing a yellow marble are 17 to 25
Below are three boxes containing black and white balls. The number of each color is noted inside the box. Draw a ball from box 1 and place it in box 2. Then draw a ball from box 2 and place it in box 3. Finally draw a ball from box 3. Box 1 5 white 2 black Box 2 2 white 3 black Box 3 3 white 0 black a) What is the probability that the last ball, drawn from...
A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events A: One of the balls is yellow B: At least one ball is red h C: Both balls are green D:Both balls are of the same color ) Find the following conditional probabilities: (a) P(BA)- b) P(DB)- (c) P(DIC)-
A ball is selected from an box containing two black balls, numbered 1 and 2, and two white balls, numbered 3 and 4. Let the events A, B, and Cbe defined as follows: A-b). (2, b)3. "black ball selected": B (2.b). (4,w)), "even-numbered ball selected": and (3, w). (4, w)). "number of ball is greater than 2." Are events A and B independent? Are events A and C independent? Please show your proofs.