If two balanced die are rolled, the possible outcomes can be represented as follows.(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6,2)(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)(1,4) (2, 4) (3, 4) (4,4) (5, 4) (6,4)(1,5) (2, 5) (3, 5) (4, 5) (5,5) (6,5)(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)Determine the probability that the sum of the dice is 11.1361/9O 1/12O 1/361/18B)18D) 1/22

Given that S={ (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1)…

Answered: If two balanced die are rolled, the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(v) A standard six-sided die is tossed twice. State the number of distinct outcomes if: (a) the sum of the two rolls is recorded. (b) the difference between the two rolls is recorded.
You're a sociologist studying whether grocery prices are different in the inner cities than they are in the suburbs. To investigate this, you pick a random set of items (a basket of goods), and then send shoppers to buy these items at an inner city (IC) grocery, and also at a suburban (SU) grocery. You pick 27 different baskets of goods, so your secret shoppers buy 27 baskets, once at the inner city store, and once at a suburban store. The data is given in the dataset named "ICvSU_2799.xls", which you can find in data folder under Course Documents. Prices could be higher in the inner city because of discrimination, or they could be higher in the suburbs because of the greater disposable income. Use Excel to test the research hypothesis that inner city prices are different than the suburb's prices. The null hypothesis is that inner city prices are equal to suburban prices. You test at the alpha = 0.01 significance level. What do you conclude? Are prices the same? Who has higher…
4) D E F
Suppose you are playing a game of Yahtzee. You know that you play with 5 dice, each with 6 sides. Since the dice are all rolled at the same time, let the roll (5, 4, 3, 2, 1) to be equal to (2, 4, 5, 1, 3). Assume for this question that we will only be rolling the dice once. (i) How many ways can you roll all the dice? (ii) To win 50 points you would need all the dice to roll the same number (ex. (1, 1, 1, 1, 1)). How many ways can you win the 50 points? (iii) Suppose you are trying to get your dice to roll only consecutive numbers (ex. (1, 2, 3, 4, 5) or (2, 3, 4, 5, 6)) How many different ways are there to do this? (iv) Suppose instead you are trying to get your dice to roll 4 consecutive numbers (ex. (1, 2, 3, 4, 1) or (2, 3, 4, 5, 3)) How many different ways are there to do this? (make sure to not count any only consecutive numbers) This is a combinatorics math counting problem.
You're a sociologist studying whether grocery prices are different in the inner cities than they are in the suburbs. To investigate this, you pick a random set of items (a basket of goods), and then send shoppers to buy these items at an inner city (IC) grocery, and also at a suburban (SU) grocery. You pick 30 different baskets of goods, so your secret shoppers buy 30 baskets, once at the inner city store, and once at a suburban store.The data is given in the dataset named "ICvSU_3095.xls", which you can find in data folder under Course Documents. Prices could be higher in the inner city because of discrimination, or they could be higher in the suburbs because of the greater disposable income. Use Excel to test the research hypothesis that inner city prices are different than the suburb's prices. The null hypothesis is that inner city prices are equal to suburban prices. You test at the alpha = 0.05 significance level. What do you conclude? Are prices the same? Who has higher prices?…
B. 3R+6B SR+4B PCR) = ? %3D P (B)= ? P( BilR)=? PC Bi |B)=? P ( Bzl R)=} P (Bz| B)= ? 2. If there are two Bqqs B, and Bz. In Bag bage one there are 3 red balls and 6 Blue bells. In Bag two there are 5 red balls andA blue balle. If One ball is Chosen at random. find the following trobubilities !
7. A new drug study was conducted by a drug company. In the study, 10 people were chosen at random to take Vitamin X for 3 months and then have their cholesterol levels checked. In addition, 10 different people were randomly chosen to take Vitamin Y for 3 months and then have their cholesterol levels checked. All 20 people had cholesterol levels between 8 and 10 before taking one of the vitamins. The drug company wanted to see which of the 2 vitamins had the greatest impact on lowering people's cholesterol. The following data was collected: Vitamin X 7.27.5 5.2 6.5 7.7 10 6.47.6 7.77.8 Vitamin Y 4.8 4.44.5 5.1 6.5 8.03.1 4.6 5.2 6.1 (a) Draw a box-and-whisker plot for both sets of data on the same number line. (b) Use the double box-and-whisker plots to compare the 2 vitamins and provide a conclusion for the drug company. (e) State the skewness of both distributions and justify your answer.
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Show that the multiplication law P(AB) = P(A/B) P(B), established for two events, may be generalized to three events as foilows; P(AOBOC) = P(A/BOC) P(B/C) P(C)
A1(1,0,7) A2(2,5,3) A3(1,8,4) A4(5,3,8) A5(7,3,5) A6(1,6,4) A7(1,4,2) A8(1,4,9)Perform k-means clustering with k=2. Pick any two random starting points.

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