Download Mar 18

VOCABULARY
Random Phenomenom
... we know the possible outcome but not the particular one which
occur
Trial
... a single realization of a random phenomenon
Outcomes
... the value of the trial
Event
... a collection of outcomes
Sample Space
... the collection of all possible outcome values
VOCABULARY (more)
Law of Large Numbers (LLN)
... the long-run relative frequency of repeated independent
events gets closer to the true relative frequency as the
number of trials increases
Independent events (slightly different than text definition)
... two events are independent if the occurrence on nonoccurrence of one of the events does not change the
probability of the other event occuring or not occuring
Probability
... a number between 0 & 1 inclusive which reports the
likelihood of an event's occurrence.
VOCABULARY (more)
Probabilities:
empirical
... from a real-life long-run relative frequency
theoretical
... from a model (think math)
personal
... a gut feeling (not in this course!)
PROBABILITY RULES (memorize)
... events denoted by A, B, C, D, E, F, ... and S for the sample
space
... P(A) in the text and Pr(A) for the probability of event A
... Pr(E) is always between 0 and 1
... Pr(AC) = Pr(A') = Pr(~A) is the probability that A does not
occur; the AC, A', and ~A denote the complement of A
... Pr(AC) = 1 - Pr(A) and Pr(A) = 1 - Pr(AC)
... Pr(AC) + Pr(A) = 1
... Pr(S) = 1
... Pr(A or B) = Pr(A) + Pr(B) if A and B disjoint events or
mutually exclusive (no overlap)
... Pr(A and B) = Pr(A)*Pr(B) if A and B are independent
Some problems with rolling a single die:
1) Pr(4) =
2) Pr(not 4) =
3) Pr(2 or 7) =
4) Pr(5 and 6) =
Some problems when rolling two dice, one red and one
green, and finding the sum.
1) Pr(2) =
2) Pr(not 2) =
3) Pr(7 or 9) =
4) Pr(7 and 9)
5) Pr(green die is 4 and red die is 6) =
red
1
2
3
4
5
6
green _____________________________________________
1 | 1 1
1 2
1 3
1 4
1 5
1 6
|
2 | 2 1
2 2
2 3
2 4
2 5
2 6
|
3 | 3 1
3 2
3 3
3 4
3 5
3 6
|
4 | 4 1
4 2
4 3
4 4
4 5
4 6
|
5 | 5 1
5 2
5 3
5 4
5 5
5 6
|
6 | 6 1
6 2
6 3
6 4
6 5
6 6
Exercises from text:
#2) List the sample space and state whether events are
equally likely.
a) roll two dice and record the sum
b) a family has 3 children; record each child's sex in order of
birth
c) toss four coins; record the number of tails
d) toss a coin 10 times; rcord the longest run of heads
#4) The weather reporter on TV makes predictions such as a
25% chance of rain. What do you think is the meaning of such
a phrase?
What kind of probability is this?
#7) A batter who had failed to get a hit in seven consecutive
times at bat then hits a game-winning home run. When talking
to reporters afterward, he says he was very confident that last
time at bat because he knew he was "due for a hit."
Comment on his reasoning.
#10) On January 20, 2000, the International Gaming
Technology company issued a press release:
(LAS VEGAS, Nev.)
Cynthia Jay was smiling ear to ear as she walked into the news
conference at The Desert Inn Resort in Las Vegas today, and
well she should. Last night, the 37-year-old cocktail waitress
won the world's largest slot jackpot -- $34,959,458 -- on a
Megabucks machine. She said she had played $27 in the
machine when the jackpot hit. Nevada Megabucks has
produced 49 major winners in its 14-year history. The top
jackpot builds from a base amount of $7 million and can be
won with a 3-coin ($3) bet.
a) How can the Desert Inn afford to give away millions of
dollars on a $3 bet?
b) Why did the company issue a press release? Wouldn't most
businesses want to keep such a huge loss quiet?
#16) Although it's hard to be definitive in classifying
people as right or left handed, some studies suggest that
about 14% of people are left handed. Since 0.14*0.14 =
0.0196 = 1.96%, the Multiplication Rule might suggest that
there's about a 2% chance that a brother and a sister are
both lefties.
What's wrong with that reasoning?
#20) In a large Introductory Statistics lecture hall, the
professor reports that 55% of the students enrolled have
never taken a Calculus course, 32% have taken only one
semester of Calculus, and the rest have taken two or more
semesters of Calculus. The professor randomly assigns
students to groups of three to work on a project for the
course.
What is the probability that the first groupmate you meet
has studied:
a) two or more semesters of Calculus?
b) some Calculus?
c) no more than one semester of Calculus?