Notes 6.1-6.2
AP Stats
Basic Probability Rules
Name__________________
Date____________Per____
Probability Definitions:
1. Chance experiment- Any activity or situation in which there is ________________ about which of
two or more possible ______________ will result.
2. Sample Space- The collection of all possible ______________ of a ____________ ___________.
3. Event- Any collection of outcomes from the sample space of a chance experiment.
4. Simple Event- An event consisting of exactly _____ outcome.
5. Mutually Exclusive(disjoint)- Two events that have no common outcomes.
6. Complementary Events- Two mutually exclusive events who’s probability add to 1.
Let A and B denote two events.
7. Not A- Consists of all experimental outcomes that are not in event A. Not
A is called the complement of A and is denoted AC, A' , or Ā.
8. The event A or B consists of all experimental outcomes that are in at least one
of the two events, that is in A or B or in both of these. A or B is called the
union of the two events and is denoted A  B.
P(A  B)=P(A)+P(B)- P(A  B)
9. The event A and B consist of all experimental outcomes that are in both of the
events A and B. A and B is called the intersection of the two events and is
denoted by A  B.
10. Probability of an event E, denoted by P(E)= favorable outcomes/total outcomes.
Let A= Probability of Rudy Gay making his only free throw in a game.
Let B= Probability of Demarcus Cousins making his only free throw in a game.
Assume Rudy shoots 90% and Demarcus shoots 70%, and the probability they both make a free
throw is 65%
11. Find the Probability of event A, P(A) and Probability of event not A, P(Ac)
____, ____
12. Find the Probability of at least one of them making a free throw.
____
13. P(only Rudy makes his free throw)
____
14. P(Ac  B)
____
15. P(exactly 1 making a free throw)
____
16. P(neither making a free throw)
____
17. As of Dec 17, 2015, Rudy actually shoots 83% and Demarcus Shoots 75%. Assume, the probability
that they both make the free throw is 68%.
a. Find the probability that at least one free throw is made.
_____
b. Find the probability that neither free throw is made.
_____
c. Find the prob that exactly 1 free throw is made.
_____
d. Find the prob that Demarcus makes his and Rudy misses his shot.
_____
18. Consider the event, a coin is flipped twice.
a. List the four possible outcomes(sample space):
____ , ____ , ____ , ____
b. Find the prob that at least one tail is tossed.
_____
c. Find the prob that no tails are tossed.
_____
19. In the GB woodshop, 60% of all machine breakdowns occur on lathes and 15% occur on drill presses.
Let E denote the event that the next machine breakdown is on a lathe, and let F denote the event that a
drill press is the next machine to break down. With P(E)= .60 and P(F)=.15 calculate:
a. P(EC)=
_____
b. P(E  F)=
_____
c. P(EC  FC)=
_____
Homework 6.1/6.2:
1. Two cars arrive at a stoplight. The probability that the first stops is 60%. The probability the second
stops is 70%. The probability they both stop is 40%.
P(A)=.6 P(B)=.7 P(A  B)=.4
a. Find P(A  B)._____
b. Find the prob that only A stops._____
c. Find the prob that exactly 1 stops. _____
d. Find the prob that neither stop. _____
e. Find the prob that B doesn’t stop. _____
2. Either Brian or Mark is responsible for cleaning the classroom after school. The probability of Mark
cleaning is 90%. The probability of Brian cleaning is 80%. The probability of both cleaning is 75%.
a. Find the prob of at least one person cleaning the classroom. _____
b. Find the prob of Brian, but not Mark cleaning the classroom. _____
c. Find the prob that exactly 1 person will clean the classroom. _____
d. Find the prob that the room will stay dirty. _____
3. The following table shows the size of the tennis racket grip and the type of racket.
4 3/8 4 ½ 4 5/8
a. P(Grip Size =4 ½)=_____
Mid Size .10 .20 .15
Oversize .20 .15 .20
b. P(Grip Size is not 4 ½)=_____ (These are complementary events)
c. P(Oversize)=_____
d. P(At least a 41/2 inch grip)=_____
4. P(A  B)= .40
P(A  Bc)= .30
P(Ac  B)=.20
a. Find P(B)=_____
b. Find P(Ac  Bc)=_____
c. Find P(A  B)=_____
5. An “honor card” is considered to be an Ace, King, Queen, or Jack. There are four of each of these cards
in a standard 52 card deck. What is the probability that I draw a card that is an honor card? _____
6. At the start of a Scrabble game you turn over the 100 lettered tiles so you can’t see them. There are four
S’s and two blanks among the 100 tiles. If you pick a tile at random, what’s the probability you will not
get a S or a blank?
7. The probability that a white adult man with high a blood cell count contracts leukemia is .35. A proper
interpretation of this probability is:
a. There’s a 35% chance that a randomly selected white adult man will contract leukemia.
b. Three out of every five white adult men with high white blood cell count will contract leukemia.
c. There’s a 65% chance that a randomly selected white adult man with a high white blood cell count
will contract leukemia.
d. We’d expect that in a sample of 100 white adult men with high blood cell counts, 35% will contract
leukemia.
e. None of the above.
8. In Sausha’s pocket, she has 7 pennies, 3 nickels, 3 dimes, 2 half dollars, and 1 dollar coin. If Sausha
selects 1 coin from her pocket, what’s the probability that it’s divisible by $0.10? (Ignore the fact that
it’s possible to distinguish the coins by the size and shape of the coin)
a. 1/3
b. ½
c. .0300
d. 0.375
e. 1/7
9. Which of the following are true?
i. Two events are mutually exclusive if they can’t both occur at the same time.
ii. The set of all possible outcomes of a probability experiment is called a simple event.
iii. An event and its complement have probabilities that always add to 1.
a.
d.
I only
I and II only
b. II only
e. I and III only
c. III only