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.
 (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 )
 (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!
B = “Exactly two letters go into the correct envelopes”
P(B) = (4
C=“Exactly three letters go into the correct envelopes”
P(C) = 0
24 = 0