Download Quiz4

Quiz 4
May 4 2004
5.1, 5.2, 5.3
Discrete Probability
Quiz 4: May-04 ’04 3.30-3.45 pm
We conduct an experiment where we roll a die 5 times. The order in which the
numbers a read out is important.
a) What is the total number of possible outcomes of this experiment.
b) What is the probability that exactly 3 times a “2” appears in the sequence (event E)
(hint: first count the number of ways you can realize a sequence with 3 “2”’s,
then count the number of each sequence can be realized.)
c) What is the probability that at least twice no “2” appears, i.e. 1,3,4,5 or 6 appears
(event F). This question will not be part of your grade.
d) Which of the following are true:
e) Compute the probabilities:
E  F, F  E
P( E  F ), P( E | F ), P( F | E )
f) Are the events E and F independent ?
Quiz 4: Answers
a) What is the total number of possible outcomes of this experiment.
6^5
b) What is the probability that exactly 3 times a “2” appears in the sequence (event E)
(hint: first count the number of ways you can realize a sequence with 3 “2”’s,
then count the number of each sequence can be realized.)
C(5,3) x 5^2 / 6^5
c) What is the probability that at least twice no “2” appears, i.e. 1,3,4,5 or 6 appears
(event F): The probability that at most 3 times a “2” appears=
5^5/6^5 + C(5,1) x 5^4/6^5 + C(5,2) x 5^3/6^5 + C(5,3) x 5^2/6^5.
prob. 0 “2”’s appear – prob. 1 “2” appears etc. until prob. 3 “2”’s appear.
d) Which of the following are true: E  F , F  E
If E happens, then F is automatically true  E is subset of F.
e) Compute the probabilities: P( E  F ), P( E | F ), P( F | E )
P( E  F )  P( E ) , P(E|F) = P(E)/P(F), P(F|E) = P(E)/P(E) = 1
f) Are the events E and F independent ?
NO!