# STAT230 Study Guide - Midterm Guide: Sample Space

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14 Nov 2012
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Short Solutions to Stat 230 Test 1, Jan 18, 2012
1. Four letters addressed to individuals W,X,Yand Zare randomly placed in four addressed envelopes,
one letter in each envelope.
[4] (a) List a 24-point sample space for this experiment. Be sure to explain your notation.
Suppose the four envelopes are arranged in a row as W XY Z. The 24 points can be listed below,
where the order of W,X,Yand Zrepresents the arrangements of four letters:
(W XY Z),(W XZY ),(W Y XZ),(W Y ZX),(W ZXY ),(W ZY X),
(XW Y Z),(XW ZX),(XY W Z),(XY ZW ),(XZW Y ),(XZY W ),
(Y W XZ),(Y W ZX),(Y ZW X),(Y ZXW ),(Y XW Z),(Y XZW ),
(ZW XY ),(ZW Y X),(ZY W X),(ZY XW ),(ZXW Y ),(ZXY W )
[3] (b) Assuming that the 24 sample points are equally likely, ﬁnd the probability of the following events:
A = “W’s letter goes into the correct envelope”
P(A) = 1×3!
24 =6
24 =1
4
B = “Exactly two letters go into the correct envelopes”
P(B) = (4
2)×1×1×1×1
24 =6
24 =1
4
C=“Exactly three letters go into the correct envelopes”
P(C) = 0
24 = 0
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