On a fence are blue jays and cardinals. When five blue jays leave, there remain two cardinals for every blue jay. Then 25 cardinals leave, and there are now three blue jays for every cardinal. Find the original number of blue jays.


On a fence are blue jays and cardinals. When five blue jays leave, there remain two...
1. An urn contains ten marbles of which five are green, two are blue, and three are red. Three marbles are to be drawn from the urn, one at a time without replacement. What is the probability that all three marbles drawn will be green? 2. In Southern California, a growing number of individuals pursuing teaching- credentials are choosing paid internships over traditional student teaching programs. A group of eight candidates for three local teaching positions con- sisted of five...
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 <...
Four balls are selected at random without replacement from an urn containing three white balls and five blue balls. Find the probability that two or three of the balls are white.
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.
23. Calculate the probability of getting exactly two sixes and one five when rolling five dice. Do this in two different ways, as follows. (a) First calculate the probability that two of the five dice land sixes, and then multiply this by the probability that one of the remaining three lands a five. (note: The remaining three dice have only five ways in which they can land.) (b) Next calculate the probability that one of the five dice lands a...
1. Live Happley should hire (one, two, three, four, or five)
worker
2. Now Live Happley should hire (one, two, three, four, or five)
workers
3. An increase in the price of strawberries will cause the
(Supply of/demand for) strawberry pickers to
(decrease/increase)
4. Live Happley will now hire (one, two, three, four, or five)
workers
4. Profit maximization Consider Live Happley Fields, a small player in the strawberry business whose production has no individual effect on wages and prices....
18. A box of animal crackers contains five hippos, two lions, three zebras, and four elephants. Find the probability if one animal cracker is chosen at random. a. Pla hippo b. P(not an elephanf) c. P(an elephant or a lion) lu 19. Suppose you have a dark closet containing seven blue shirts, five yellow shirts, and eight white shirts. You pick two shirts at random from the closet. Find each probability. a. P(blue then yellow) with replacing b. P(blue then...
Consider the following problem: How many ways are there to paint 10 identical houses on a street with five colors if at most three houses can be painted blue, at most three can be painted green, at most three can be painted beige, and no constraint is placed on the other two colors, brown and gray? A student claims that the generating function for this problem is g(x) = (1 + x +x2 + r3)3(1 + x + r2 +...
You have two fair 6-sided dice. One is red and the other is blue. When you roll them X=red-blue and Y=red+blue. a) Find the joint distribution of (X,Y). b) Find the covariance of X and Y
You are working with an ornamental fish that shows two color phenotypes, red or blue. The color is controlled by a single gene. These fish are hermaphrodites-meaning they can either (1) self-fertilize or (2) mate with another fish. You have three fish: fish 1, fish 2, and fish 3. While working further with this fish, you discover one other mutation (in a different gene) that leads to the recessive phenotype of long dorsal fins. Further research establishes that the genes...