http://www.math.ilstu.edu/krzysio/
Krzys’ Ostaszewski
Author of the BTDT Manual for Course P/1
available at http://smartURL.it/krzysioP or http://smartURL.it/krzysioPe
Instructor for online Course P/1 seminar: http://smartURL.it/onlineactuary
Exercise for April 23, 2005
Three fair dice are rolled and X is the smallest number of the three values resulting (if
more than one value is the smallest one, we still use that value). Find Pr ( X = 3) .
A.
36
216
B.
37
216
C.
38
216
D.
39
216
E.
40
216
Solution.
Pr ( X = 3) is the same as the probability that all three dice show a 3 or more, and at least
one shows a 3. This means that the event of all three showing at least 3 happened, but the
event of all three of them showing at least a 4 did not happen. This probability is:
3
3
8 1 64 ' 27 37
! 2$
! 1$
'
=
' =
=
.
#" &%
#" &%
!
2
27
8
216
216
3
BUT
NOT
!
!
ALL THREE SHOW 3,4,5 OR 6
ALLTHREE SHOW 4,5, OR 6
Answer B.
© Copyright 2005 by Krzysztof Ostaszewski.
All rights reserved. Reproduction in whole or in part without express written
permission from the author is strictly prohibited.