2. There are two boxes. Box A has 3 white chips and 1 red chip, Box B has 2 white chips and 1 red chip.There is a 40% chance that Box A will be the first box selected (that is, there is a 60% chance thatBox B will be selected first.)A box is chosen at random. From the first box chosen, a chip is selected at random, the color isobserved, and then the chip is placed in the other box (the one not chosen first). A chip is thenselected at random from the other box and the color is observed.a.C.Find the probability of observing 2 red chips in a row.b. Find the probability of observing a white chip from the other box (the last boxchosen).Given that one observes a white chip from the other box, find the probability thatBox A was the first box chosen.

In this case, color Box A has 3 color W chips and 1 color R chip.

Answered: 2. There are two boxes. Box A has 3…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1
8) In a class of 100 half the students are science majors and half are liberal art majors. A student who is a science major has a 0.9 probability of passing a given test whilst a student who is liberal art major has only a probability of 0.7. We pick 2 students at random without replacement and give them the test. What is the probability that both students pass the exam?
In a random sample of 1,000 people, it is found that 7% have a liver ailment. Of those who have a liver ailment, 40% are heavy drinkers, 50% are moderate drinkers, and 10% are nondrinkers. Of those who do not have a liver ailment, 10% are heavy drinkers, 70% are moderate drinkers, and 20% are nondrinkers. If a person is chosen at random and he or she is a heavy drinker, what is the probability of that person having a liver ailment? What is the probability for a nondrinker?
2. A kindergarten class has 6 boys and 7 girls. At the end of each day, the teacher selects 5 students, uniformly at random, and asks them to help clean up the classroom. One of the boys in the class is named Vito. Show that, with probability = 38%, Vito and at least one girl will be amongst the 5 students asked to clean up today.
30. The chess clubs of two schools consists of, respectively, 8 and 9 players. four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that exactly one of Rebecca and Elise will be chosen to represent her school? Show the STEP-BY-STEP SOLUTION CLEARLY. SHOW EXPLAMATIONS IF NECESSARY.
4. A newspaper story claims that more houses are purchased by singles now than singles 5 years ago. To test this claim, two studies were conducted on the buying habits of singles over the past 5 years. In the first study, 200 house purchases in the current year were randomly selected and 80 of those were made by singles. In the second study, again 200 house purchases were randomly selected from 5 years ago and 57 of those were made by single people. Test the newspaper's claim using a 0.05 level of significance. Is there sufficient evidence to support the newspaper's claim? Let singles now be Population 1 and let singles 5 years ago be Population 2. Step 1. State the null and alternative hypotheses for the test. Fill in the blank below. A) Step 2. Compute the value of the test statistic. Round your answer to two decimal places. Step 3. Draw a conclusion and interpret the decision. A) We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level…
Bag 1 contains 8 gray rocks and 5 black rocks, and Bag 2 contains 9 gray rocks and 4 black rocks. Suppose we flip a fair coin. If the result is heads, we randomly select a rock from Bag 1; if the result is tails, we randomly select a rock from Bag 2. Suppose that a gray rock was selected. What is the probability that the rock came from Bag 1?
There are three containers, A, B and C. Each container contains 25 balls, which are either red or blue. Container A has 15 red balls, container B has 16 red balls, and container C has 12 red balls. In a random experiment, one first randomly chooses a container, and then a ball is drawn from the chosen container. The probability of choosing container B in step 1 is 2/5 . The experiment is designed so that the events “the ball drawn is red” and “the ball drawn comes from container A” are independent. Suppose that the ball drawn is red. What is the probability that it came from container C?
Three groups of children contain respectively 3 girls and I boy: 2 girls and 2 boys: 1 girl and 3 boys. One child is selected at random from each group, Show that the chance that the three selected consist of 1 girl and 2 boys is 13/32?

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