PROBLEM: Marbles in a Box Suppose there are 17 marbles in a box. There are 5...
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)
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...
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...
Problem 3. Consider a box with three blue and five red marbles. Suppose draws are made from the box with replacement until two red marbles are drawn. Let Y denote the number of draws required, and let X denote the number of draws it takes to obtain the first red marble. (1) Calculate P(X-s, Y t) for integers s and t, 1 3 (2) Use the above to find P(Y t). (3) Calculate P(X = sy-t) for 1 s <...
A box of marbles has 5 red marbles, 2 green marbles, and 1 blue marble 5. A box of marbles has 5 red marbles, 2 green marbles, and 1 blue marble. (a) Find the probability of selecting 2 red marbles if the first selection is replaced before the next selection is made. (b) Find the probability of selection 2 red marbles if the first selection is not replaced before the next selection is made (c) Find the probability of selecting...
In a box, there are 400 blue marbles and 100 red marbles. When 200 marbles are randomly chosen from the box, let the random variable X represent the number of chosen blue marbles. (a) [10 points) Find P(X > 102). [You may leave the answer in terms of "combinations” or “factorials”.) (b) [10 points) Find P(X = 160) using binomial approximation.
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?
5. There are 7 red marbles and 3 blue ones in a jar. We randomly take out marbles from the jar without replacement, which means that we do not put any marbles back into the jar after they are taken out. MATH 32: Probability & Statistics Fall Semester 2019 (a) We take out 3 marbles. Let X be the number of red marbles among the three. Does X have a binomial distribution? Why or why not? (b) Let Y be...
#2 1. Suppose a box contains 4 red marbles and 4 green marbles. If you select 3 marbles with replacement what is the probability of getting all red marbles Answer: Here the and is implied. You need to get and a red on the third Since we are selecting with replacement, the events a red on the first and a red on the second PlRi and R and R) = p(R)、P(R,) , p(Rs) = 8 = (5) 2. Suppose you...
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...