IE 111 Fall 2007
Homework #3
Due Beginning of Class on Monday 9/24
Question 1
Suppose we have a biased coin such that P(head)
≠
P(tail).
Suppose I flip the coin three
times.
Let the random variable X be the number of heads in the 3 flips.
You are given
the following information:
P(X=0) = 1/27
P(X=1) = 6/27
P(X=2) = ?
P(X=3) = 8/27
a) Find P(X=2)
b) Find P( 1
≤
X < 2)
c) Find P( X=1  X
≤
1)
Question 2
Three fair coins are tossed.
Find the following:
a) P(TTH)
b) P(more heads than tails)
c) P(more heads than tails  at least one tail)
d) P(Exactly one head  at least two tails
Question 3
Suppose that P(AB) = 0.3
and P(B) = 0.5.
Find:
a)
P(A and B)
b)
P(A
′
and B)
Question 4
Three events A, B, and C are independent with the following probabilities:
P(A)=0.6
P(B)=0.4
P(C)=0.2
a)
What is the probability that at least one of the three events occurs?
b) Find P(AC)
c)
Find the probability that exactly two of the events occur.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentQuestion 5
If P(AB)=0.4, P(B)=0.8, and P(A)=0.4, are
events B and A
′
independent? Prove it.
Question 6
I have 2 identical six sided dice.
The dice are fair in that each of the six sides is equally
likely to come up.
The only difference between these dice and regular dice is that three
sides are labeled "1", two sides are labeled "2" and one side is labeled "3" (this is true for
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '07
 Storer

Click to edit the document details