Problem 3. Consider a box with three blue and five red marbles. Suppose draws are made...
There is a box of 20 marbles. Of these marbles, 6 are red, 8 are green and 6 are blue. 6 marbles are randomly selected from the box without replacement. Let X be the number of marbles that are red or blue, and let Y be the number of marbles that are blue. a. What is the probability the first and second marbles are red, the third and fourth are blue and the fifth and sixth are green? b. What...
Suppose that a drawer contains 8 marbles: 2 are red, 2 are blue, 2 are green, and 2 are yellow. The marbles are rolling around in a drawer, so that all possibilities are equally likely when they are drawn. Alice chooses 2 marbles without replacement, and then Bob also chooses 2 marbles without replacement. Let Y denote the number of red marbles that Alice gets, and let X denote the number of red marbles that Bob gets. a. Find the...
A box contains 3 red and 4 green marbles. Five marbles are drawn without replacement. Let X denote the number of red marbles obtained. a) Construct the probability distribution of X. b) What is the expected number of red marbles?
If we were to have a box of marbles containing 2 red, 2 black, 2 blue, and 2 yellow, and we drew out a marble, we would then have the choice of keeping the marble out or putting it back. Each choice affects the odds (probability) of subsequent draws differently. If we draw out a red marble and put it back, this is known as with replacement, and the odds of subsequent draws are the same is for the first...
5. Three boxes are numbered 1, 2 and 3. For k 1, 2, 3, box k contains k blue marbles and 5 - k red marbles. In a two-step experiment, a box is selected and 2 marbles are drawn from it without replacement. If the probability of selecting box k is proportional to k, then the probability that two marbles drawn have different colours is 6. Two balls are.dropped in such a way that each ball is equally likely to...
Suppose that a box is known to contain 50 red and 25 blue marbles. Two marbles are to be drawn in succession. The first marble is set aside and its color noted. It is not placed back into the box before the second marble is drawn. a. Sketch a probability tree which represents this situation. b. What is the probability that the second marble is red, if the first marble is red?
PROBLEM: Marbles in a Box Suppose there are 17 marbles in a box. There are 5 blue marbles, 4 yellow marbles, 3 red marbles, and 5 green marbles. The experiment is selecting 2 marbles randomly from the box, without replacement. Let x be the number of blue marbles. Note: The picture shown is an example of marbles in the box. The number of marbles and their color code does not reflect to this problem (a) Determine whether the experiment is...
A box contains 10,000 marbles, of which some are red and the others blue. To estimate the percentage of red marbles in the box, 100 are drawn at random without replacement. Among the draws, 1 turns out to be red. The percentage of red marbles in the box is estimated as 1%, with an SE of 1%. True or false: a 95%-confidence interval for the percentage of red marbles in the box is 1% ± 2%. Explain.
A jar contains 9 red marbles, 7 green marbles, and 5 blue marbles. 34. If a single marble is drawn from the bag, what is the probability that it is red? (3 pts) 35. If three marbles are drawn without replacement, what is the probability that all three Subles are green? [4 pts) 36. I samarbles are drawn with replacement, what is the probability that at least 1 blue marble was selected. 5 pts
1. A box contains 3 marbles: 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. Describe the sample space. Repeat when the second marble is drawn without replacing the first marble.