P(L and P)
0.429
P(D or P)
0.908
P(L or D)
1.00
P(P')
0.418
P(P|L)
0.824
P(L|P)
0.737
Formula for P(A|B)
P(A|B) = P(A and B) / P(B)
The addition rule
Formula for P(A or B)
P(A or B) = P(A) + P(B) - P(A and B)
List the sample space for flipping a coin four times
{HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}
The multiplication rule
Formula for P(A and B)
P(A and B) = P(A)*P(B|A)
A _______ ______ is an event that cannot be further broken down
simple event
An _______ is a collection of results or outcomes of a procedure
event
The ________ of an event tells us how likely that event is to occur, values lie between __ and __ , the smaller the value the less likely the _____ to occur
probability
0
1
event
The _____ _____ consists of all possible simple events
sample space
Flipping a coin three times and getting {H H H} is an ____ and a _____ _____ because there is only ____ way to get three heads in three coin flips
event
simple event
one
Flipping a coin three times and getting 2 heads and 1 Tails is an _____ , but not a _____ _____ because the pattern could have occurred as HTH, HTH, or HTH
event
simple event
A deck of cards has
____ cards total
____ red cards
____ red diamonds
____ red hearts
____ black cards
____ black spades
____ black clubs
of the 13, they are numbered as [____] , where __, __, and __ are face cards
__ is not a face card
52
26
13
13
26
13
13
2,3,4,5,6,7,8,9,10
J Q K
A
A _______ _______ is made up of more than one simple event
compound event
The ____ ____ ______ _____ refers to how the more times a procedure is repeated, the closer it is to the true probability
law of large numbers
Properties of probabilities
For ___ _____ ___ , 0 ≤ P(A) ≤ 1
any event A
Properties of probabilities
If P(A) = 0, then A is an _______ _______
impossible event
If P(A) = 1, then A is a ______ _______
certain event
An event is unlikely if P(A) ≤ _____
0.05
Two events A and B are independent if and only if:
_____ __ ____
Because A is not impacted by the probability of B
_______ __ ___
Because B is not impacted by the probability of A
___________ __ ___ __ ____
P(A|B) = P(A)
P(B|A) = P(B)
P(A and B) = P(A) * P(B)
Independent events
Two events, A and B, are __________ if the occurrence of one _______ affect the probability of the occurrence of the other
If two events are not independent they are called _________
independent
does not
dependent
With replacement
Each member of the population is replaced after it is picked, so the member has the possibility of being chosen more than once
When sampling is done with replacement, the events are _____________
independent
Without replacement
Each member of the population may only be chosen once
In this case, the probabilities for the second pick are affected by the result of the first pick, so they are ___________
dependent
Mutually exclusive events
Two events A and B are mutually exclusive or disjoint if they cannot occur at the same time
Mutually exclusive if _________ __ ___
If they A and B are mutually exclusive, then __________ __ _____ _ _____
P(A and B) = 0
P(A or B) = P(A) + P(B)
If one person is randomly selected, find the probability that their birthday is not in may (ignore leap years)
0.915
Consider a sample of 5 pacemakers, 3 that are good and 2 that are defective, find the probability that two are selected at random and the first one is good and the second one is good
a) assume the two selected are with replacement
b) assume the two are selected without replacement
0.360
0.300
Assume two people are randomly selected and also assume that birthdays occur on the days of the week with equal frequencies.
a) Find the probability that two people are born on the same day of the week
b) Find the probability that two people are born on Monday
0.143
0.0204
The probability of an electric system failure is 0.001.
a) If the engine in an aircraft has one electrical system, what is the probability that it will work
b) If the engine has two independent electrical systems, what is the probability that the engine can function with a working electrical system
0.999
0.99999