1
Assignment 2, STAT220Winter 2011
Instructor: Kamyar Moshksar
Due on
Wednesday, Feb. 9th
Problem 1
 In your course notes, you can find the following identity at the end of section 3 in the
“Review of Useful Series and Sums” subsection:
min
{
a,n
}
X
x
=max
{
0
,n

b
}
a
x
b
n

x
=
a
+
b
n
.
(
*
)
This identity is proved in your course notes using Binomial Expansion. In this problem, you will prove
this identity probabilistically.
We have a box that contains
a
+
b
bulbs where
a
bulbs are defective and the rest (
b
bulbs) are fine. We
pick
n
bulbs at random.
(a) what is the probability that exactly
x
of the
n
picked bulbs are defective?
(b) Prove the identity in (*) using the result in part (a).
Problem 2
We have a coin with the property that
P(
Head
) =
p
and
P(
Tail
) = 1

p
. This coin is
tossed repeatedly and independently until a Tail appears for the first time. Find the probability that the
number of required tosses is even?
Problem 3
A standard pack of cards has 52 cards, 13 in each of four suits. Suppose 4 players are
dealt 13 cards each from a wellshuffled pack. What is the probability of dealing a perfect hand? (13 of
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 Fall '08
 Burbidge,John
 Conditional Probability, Probability, Probability theory, Playing card, Suit

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