Steven Weber
Dept. of ECE
Drexel University
ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2010)
Recitation 2 Solutions
Please answer any two of the following four questions. Indicate clearly which two questions you wish to be graded.
1.
A fair sixsided die is rolled three times independently. Which is more likely: a sum of
11
or a sum of
12
?
An 11 may occur 27 ways, while a 12 may occur 25 ways, hence an 11 is more likely:
146
155
164
236
245
254
263
326
335
344
353
362
416
425
434
443
452
461
515
524
533
542
551
614
623
632
641
,
156
165
246
255
264
336
345
354
363
426
435
444
453
462
516
525
534
543
552
561
615
624
633
642
651
(1)
2.
We deal from a wellshuffled
52
card deck. Calculate the probability that the
13
th card is the first king to be
dealt.
The event that the first king is drawn on the 13th card means the first 12 cards are not kings and the 13th
card is a king. Since ordering is important, we work with permutations:
P
12
,
48
×
P
1
,
4
P
13
,
52
=
4 48! 39!
36! 52!
=
703
20825
≈
0
.
0337575
.
(2)
3.
Ninety students, including Joe and Jane, are to be split into three classes of equal size, and this is to be done
at random. What is the probability that Joe and Jane end up in the same class?
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 Spring '04
 Eisenstein
 Self number, 496, 175, 13th card

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