STAT230
FINAL EXAMINATION
FALL 2000
1. Stat230 has six sections in Fall 2000. Five friends take this course and each of them chooses a
section at random.
(a) [4] Calculate the probability that they are all in the same section.
(b) [4] Calculate the probability that they are all in different sections.
(c) [4] Calculate the probability that two of them are in one section, and the other three are in other
three different sections.
2. A box contains 6 red balls and 9 blue balls. All balls are distinguishable. Let
X
= the number of
red balls among 10 randomly selected balls from the box;
Y
= the total number of balls selected from
the box to get the first red ball.
(a) [4] Suppose balls are selected
with
replacement, give expressions for
(i) the probability function of
X
.
(ii) the probability function of
Y
.
(b) [4] Suppose balls are selected
without
replacement, give expressions for
(i) the probability function of
X
.
(ii) the probability function of
Y
.
(c) [4] Suppose 5 yellow balls are added to the box, so the box contains 6 red, 9 blue and 5 yellow
balls. Twelve balls are selected at random from the box
with replacement
, let
X
1
,
X
2
and
X
3
be the number of red, blue and yellow balls selected, respectively.
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 Fall '06
 various
 Probability, Probability theory, twelve months, one hour, 60 minutes, 500ml, 100mL

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