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class 1 > 4.6 review issues > Flashcards

4.6 review issues Flashcards

1
Q

what is another name for sample point

A

Experimental outcome

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2
Q

What is a sample Space

A

set of all experimental outcomes

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3
Q

Multistep experiments what is the easy formula

A 
toss = trial 
variable = # of outcomes

x = variable 
y = # of trials

X to the exponent y

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4
Q

What are mutually exclusive events

A
  • they do not have any sample points in common
  • if one event occurs, the other CANNOT Occur
  • their intersection must contain no sample points
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5
Q

What is the addition law for mutually exclusive events

A

P(AUB) = P(A) + P(B)

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6
Q

Joint prob dependent events doesP A|B = P(A)?

A

no

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7
Q

Joint prob independent events does P(A|B) = P(A)

A

yes and P(B|A) = P(B)

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8
Q

If P(AnB) = P(A)P(B) then A and B are

A

independent

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9
Q

If P(AnB) does not equal P(A)P(B) then

A

they are dependent

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10
Q

Can 2 events with nonzero probabilities be both mutually exclusive and independent?

A

no

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11
Q

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)

A

cannot occur

The prob of the other event occurring is zero

and they are therefore, dependent

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12
Q

The total of two complementary events =

A

1

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13
Q

The sum of all experimental outcomes =

A

1

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14
Q

Describe the relative frequency method for assigning probabilities

A

experimentation or historical data is used

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15
Q

What does nonzero probability mean

A

just means its positive probability

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16
Q

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

A

.3

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17
Q

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

A

.6

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18
Q

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

A

0

if B happens then A cannot happen.

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19
Q

if you roll a die 4 times, the prob of obtaining a 6 two times is what

A

the prob of each one is 1/6

so for 4 rolls, we multiply 1/6 x 1/6 x1/6 x 1/6

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20
Q

If P(AnB) does not equal zero then is it mutually exclusive or not mutually exclusive

A

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

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21
Q

If P(A|B) does not equal P(A) then what can be said about this

A

Then A and B are dependent. In order for them to be independent, P(A|B) = P(A)

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22
Q

If you want to know if A and B are mutually exclusive, what can you use other than a diagram

A

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

23
Q

If you want to know if A and B are Indepdendent, what can you used other than a diagram

A 
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
24
Q

If P(AnB) = zero, what can be said about this

A

it is mutually exclusive

25
If P(AnB) = 4, what can be said about this
it is not mutually exclusive, they share some points
26
If P(A) = 5 and the P(A|B) = 5, then what can be said about this
they are independent
27
If P(A)= 5 and the P(A|B) = 10, then what can be said about this
they are dependent
28
What are two compliment events
A and Ac
29
what is the sum of two compliment events
A + Ac = 1
30
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)
31
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
32
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
33
another name for an experimental outcome is
a sample point
34
What is the sum of k experimental outcomes
sumP(Ei) = 1
35
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
36
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
37
How do you determine the total number of sample points in the sample space say 3 bags with 10 marbles in each bag
1. first bag has 10 2. second bag has 10 3. third bag has 10 10 x 10 x 10 =1000
38
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
39
6 sided die is tossed two times, the prob of getting two 1s is
answer
40
If A & B are mutually exclusive thenP(AuB) =
0
41
if you have an experiment that has 4 outcomes or sample points what is the total of all sample points
1
42
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
43
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
44
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)
45
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
46
Two events A and B. Are they independent or Dependent P(A| B)=P(A|B')
Independent
47
Two events A and B. Are they dependent or independent P(B∣A)=P(B∣A′)
Independent
48
The example of removing marbles from a bag without replacing them is dependent or independent?
Dependent
49
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)
50
Calculate the Prob of A|B) for an independent event
P(A|B) = P(A)
51
Calculate the Prob of A|B) for an independent event
P(A|B) = P(A)
52
for independent events how do you calculate the P(b) You know the following: P(A), P(AandB)
P(B) = P(AnB) / P(A)
53
The union of two events with nonzero probabilities can / cannot be
mutually exclusive and independent
54
If the prob A and Prob B = P(AnB) then what can be said (independent or dependent)
Independent events

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