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
If P(AnB) = 4, what can be said about this
it is not mutually exclusive, they share some points
If P(A) = 5 and the P(A|B) = 5, then what can be said about this
they are independent
If P(A)= 5 and the P(A|B) = 10, then what can be said about this
they are dependent
What are two compliment events
A and Ac
what is the sum of two compliment events
A + Ac = 1
If A and B are independent events what is the formula to find P(B) if we know that P(A) and P(AnB)
P(B) = P(AnB) / P(A)
How do you find sample points using an equation
example 3 children, can be either good or bad.
x = good or bad (variable)
y = 3 children (trial)
x to the exponent y
3 to the exponent 2 = 8
How do you determine the number of experimental outcomes
same as for sample points
and outcome is a sample point
x to the exponent of y
where x is the number of variables
y is the number of trials
another name for an experimental outcome is
a sample point
What is the sum of k experimental outcomes
sumP(Ei) = 1
If you toss a coin 5 times what is the prob(likelihood) of getting 5 heads in a row
use multiplication for each trial P(trial 1) = 1/2 P(trial2) = 1/2 P(trial 3) = 1/2 P(trial 4) = 1/2 P(trial 5) = 1/2
thefore, 1/2 x1/2 x 1/2x 1/2 x 1/2 = 0.3125
If A and B are mutually exclusive then how do you calculate P(AUB)
think about drawing the two circles, they do not touch if they are ME
so, their intersection = 0
and their union = ( Union indicates adding so) P(A) + P(B) sum of A and B
How do you determine the total number of sample points in the sample space say 3 bags with 10 marbles in each bag
- first bag has 10
- second bag has 10
- third bag has 10
10 x 10 x 10 =1000
In an experiment where A and B are mutually exclusive, the sum of P(A) and P(B) must equal ________. So if P(A) is .4 then the P(B) must be________
1
.6
6 sided die is tossed two times, the prob of getting two 1s is
answer
If A & B are mutually exclusive thenP(AuB) =
0
if you have an experiment that has 4 outcomes or sample points what is the total of all sample points
1
If you have an experiment that has 4 outcomes or sample points with the following probabilities, E1 = .1, E2 = .4, E3 = .1 then E4 would equal
.4
the sum of all sample points = 1
If A and B are mutually exclusive with P(A)= .3 P(B) = .32, then P(A|B)=
0
because if B happens, then A cannot happen
A and B are independent events
If you know the prob of A and the Prob of P(AnB) then how do you find the P(B)?
P(B) = P(ANB) / P(A)
A and B are independent events
If you know the prob of A is .45 and the Prob of P(AnB) is .3 then how do you find the P(B)?
P(AnB) / P(A)
.3/.45
Two events A and B. Are they independent or Dependent
P(A| B)=P(A|B’)
Independent
Two events A and B. Are they dependent or independent
P(B∣A)=P(B∣A′)
Independent
The example of removing marbles from a bag without replacing them is dependent or independent?
Dependent
Calculate the Prob of (A and B) for a DEPENDENT event
intersection / multiplication rule
P(AnB) = P(B)x P(A|B)
or
P(Anb) = P(A)x P(B|A)
Calculate the Prob of A|B) for an independent event
P(A|B) = P(A)
Calculate the Prob of A|B) for an independent event
P(A|B) = P(A)
for independent events how do you calculate the P(b)
You know the following:
P(A), P(AandB)
P(B) = P(AnB) / P(A)
The union of two events with nonzero probabilities can / cannot be
mutually exclusive and independent
If the prob A and Prob B = P(AnB) then what can be said (independent or dependent)
Independent events
