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!
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 Spring '04
 Eisenstein
 Self number, 496, 175, 13th card

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