4.6 review issues Flashcards
what is another name for sample point
Experimental outcome
What is a sample Space
set of all experimental outcomes
Multistep experiments what is the easy formula
toss = trial variable = # of outcomes
x = variable y = # of trials
X to the exponent y
What are mutually exclusive events
- they do not have any sample points in common
- if one event occurs, the other CANNOT Occur
- their intersection must contain no sample points
What is the addition law for mutually exclusive events
P(AUB) = P(A) + P(B)
Joint prob dependent events doesP A|B = P(A)?
no
Joint prob independent events does P(A|B) = P(A)
yes and P(B|A) = P(B)
If P(AnB) = P(A)P(B) then A and B are
independent
If P(AnB) does not equal P(A)P(B) then
they are dependent
Can 2 events with nonzero probabilities be both mutually exclusive and independent?
no
If one Mutually exclusive event is know to occur the other ___________ therefore, the prob of the other event occurring is__________ and they are therefore (independent or dependent)
cannot occur
The prob of the other event occurring is zero
and they are therefore, dependent
The total of two complementary events =
1
The sum of all experimental outcomes =
1
Describe the relative frequency method for assigning probabilities
experimentation or historical data is used
What does nonzero probability mean
just means its positive probability
If events A and B are independent and the prob of A is .3 and the prob of B is .6 what is the prob of A|B
.3
if events A and B are independent and the prob of A is .3 and the prob of B is .6 then what is the prob of B|A
.6
If event A and B are mutually exclusive and Prob of A is .3 and the prob of B is .6 then P(A|B) would be what? Explain your answer
0
if B happens then A cannot happen.
if you roll a die 4 times, the prob of obtaining a 6 two times is what
the prob of each one is 1/6
so for 4 rolls, we multiply 1/6 x 1/6 x1/6 x 1/6
If P(AnB) does not equal zero then is it mutually exclusive or not mutually exclusive
It is not mutually exclusive. In order to be mutually exclusive, P(AnB) needs to be 0 meaning that they have no sample points shared
If P(A|B) does not equal P(A) then what can be said about this
Then A and B are dependent. In order for them to be independent, P(A|B) = P(A)
If you want to know if A and B are mutually exclusive, what can you use other than a diagram
if P(AnB) is zero then it is mutually exclusive (no shared points) but
if P(AnB) is anything but zero then it is not ME
If you want to know if A and B are Indepdendent, what can you used other than a diagram
If P(A|B) = P(A), then it is independent but if the P(A|B) does not equal P(A), then it is dependent
If P(AnB) = zero, what can be said about this
it is mutually exclusive