**Problem 1**

An urn contains 40 balls, of which 18 are red and the other 22 blue. Suppose you take out 12 balls from this urn, without replacement. What is the probability that exactly 5 are red and 7 are blue among the 12 balls you choose?

**Problem 2**

Ten chairs in a row are to be occupied by seven students and Professors Alpha, Beta, and Gamma. These three professors arrive before the seven students and decide to choose their chairs so that each professor will be between two students. In how many ways can Professors Alpha, Beta, and Gamma choose their chairs?

**Problem 3**

Eight people get into an elevator at the ground floor of a hotel which has 11 upper floors. Assuming each person gets off at a randomly chosen floor, what is the probability that no two people get off at the same floor?

**Problem 4**

A random variable X is binomially distributed with mean 6 and variance 4.2. What is P(X ≤ 5)?

**Problem 5**

Each student is likely to be absent from a class 15% of the time. A class is cancelled if the number of attendants is not more than 11 out of the total registered 100. What is the expected numbers present in a class and what is the probability that a class will be canceled?

**Problem 6**

Answer the following problem from Bertsimas, Dimitris, and Robert Freund. *Data, Models, and Decisions: The Fundamentals of Management Science*. Charlestown, MA: Dynamic Ideas, 2004. ISBN: 9780975914601.

Chapter 4, p185

**Housing Prices in Lexington, Massachusetts**

** **

** **

** **

** **

** **

**Table 4.6: VALMAX Sales**

House |
Asking Price |
Selling Price |
Difference |

Number |
($) |
($) |
($) |

1 |
290,000 |
275,000 |
15,000 |

2 |
315,000 |
314,000 |
1,000 |

3 |
299,000 |
310,000 |
-11,000 |

4 |
615,000 |
610,000 |
5,000 |

5 |
345,000 |
345,000 |
0 |

6 |
230,000 |
221,000 |
9,000 |

7 |
420,000 |
418,000 |
2,000 |

8 |
399,000 |
382,000 |
17,000 |

9 |
549,000 |
555,000 |
-6,000 |

10 |
299,000 |
292,000 |
7,000 |

11 |
430,000 |
431,000 |
-1,000 |

12 |
330,000 |
303,000 |
27,000 |

13 |
395,000 |
381,000 |
14,000 |

14 |
675,000 |
661,000 |
14,000 |

15 |
460,000 |
443,000 |
17,000 |

16 |
437,000 |
449,000 |
-12,000 |

17 |
680,000 |
668,000 |
12,000 |

18 |
380,000 |
385,000 |
-5,000 |

19 |
325,000 |
310,000 |
15,000 |

20 |
435,000 |
435,000 |
0 |

21 |
304,000 |
300,000 |
4,000 |

22 |
552,000 |
560,000 |
-8,000 |

23 |
403,000 |
389,000 |
14,000 |

24 |
419,000 |
425,000 |
-6,000 |

25 |
227,000 |
217,000 |
10,000 |

26 |
340,000 |
342,000 |
-2,000 |

27 |
619,000 |
615,000 |
4,000 |

28 |
312,000 |
308,000 |
4,000 |

29 |
320,000 |
319,000 |
1,000 |

30 |
299,000 |
270,000 |
29,000 |

31 |
289,000 |
280,000 |
9,000 |

32 |
316,000 |
319,000 |
-3,000 |

33 |
328,000 |
320,000 |
8,000 |

34 |
610,000 |
615,000 |
-5,000 |

35 |
350,000 |
353,000 |
-3,000 |

** **

** **

** **

**Table 4.7: Others Sales**

House |
Asking Price |
Selling Price |
Difference |

Number |
($) |
($) |
($) |

1 |
295,000 |
280,000 |
15,000 |

2 |
425,000 |
411,000 |
14,000 |

3 |
299,000 |
285,000 |
14,000 |

4 |
299,000 |
299,000 |
0 |

5 |
475,000 |
471,000 |
4,000 |

6 |
350,000 |
348,000 |
2,000 |

7 |
429,000 |
418,000 |
11,000 |

8 |
399,000 |
401,000 |
-2,000 |

9 |
489,000 |
476,000 |
13,000 |

10 |
299,000 |
270,000 |
29,000 |

11 |
539,000 |
531,000 |
8,000 |

12 |
225,000 |
214,000 |
11,000 |

13 |
749,000 |
735,000 |
14,000 |

14 |
689,000 |
664,000 |
25,000 |

15 |
469,000 |
476,000 |
-7,000 |

16 |
299,000 |
270,000 |
29,000 |

17 |
539,000 |
531,000 |
8,000 |

18 |
199,000 |
205,000 |
-6,000 |

19 |
349,000 |
335,000 |
14,000 |

20 |
689,000 |
687,000 |
2,000 |

21 |
485,000 |
479,000 |
6,000 |

22 |
299,000 |
285,000 |
14,000 |

23 |
305,000 |
275,000 |
30,000 |

24 |
479,000 |
469,000 |
10,000 |

25 |
699,000 |
677,000 |
22,000 |

26 |
339,000 |
325,000 |
14,000 |

27 |
195,000 |
209,000 |
-14,000 |

28 |
539,000 |
535,000 |
4,000 |

29 |
279,000 |
268,000 |
11,000 |

30 |
459,000 |
469,000 |
-10,000 |

31 |
679,000 |
659,000 |
20,000 |

32 |
729,000 |
725,000 |
4,000 |

33 |
215,000 |
214,000 |
1,000 |

34 |
539,000 |
525,000 |
14,000 |

35 |
289,000 |
270,000 |
19,000 |

36 |
479,000 |
469,000 |
10,000 |

37 |
389,000 |
390,000 |
-1,000 |

38 |
419,000 |
410,000 |
9,000 |

39 |
339,000 |
339,000 |
0 |

40 |
469,000 |
462,000 |
7,000 |

41 |
299,000 |
280,000 |
19,000 |

42 |
289,000 |
280,000 |
9,000 |

43 |
419,000 |
403,000 |
16,000 |

44 |
289,000 |
275,000 |
14,000 |

Subject | Mathematics |

Due By (Pacific Time) | 07/18/2015 12:00 am |

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