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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
Q

If P(AnB) = 4, what can be said about this

A

it is not mutually exclusive, they share some points

26
Q

If P(A) = 5 and the P(A|B) = 5, then what can be said about this

A

they are independent

27
Q

If P(A)= 5 and the P(A|B) = 10, then what can be said about this

A

they are dependent

28
Q

What are two compliment events

A

A and Ac

29
Q

what is the sum of two compliment events

A

A + Ac = 1

30
Q

If A and B are independent events what is the formula to find P(B) if we know that P(A) and P(AnB)

A

P(B) = P(AnB) / P(A)

31
Q

How do you find sample points using an equation

A

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
Q

How do you determine the number of experimental outcomes

A

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
Q

another name for an experimental outcome is

A

a sample point

34
Q

What is the sum of k experimental outcomes

A

sumP(Ei) = 1

35
Q

If you toss a coin 5 times what is the prob(likelihood) of getting 5 heads in a row

A 
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
Q

If A and B are mutually exclusive then how do you calculate P(AUB)

A

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
Q

How do you determine the total number of sample points in the sample space say 3 bags with 10 marbles in each bag

A
  1. first bag has 10
  2. second bag has 10
  3. third bag has 10

10 x 10 x 10 =1000

38
Q

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________

A

1

.6

39
Q

6 sided die is tossed two times, the prob of getting two 1s is

A

answer

40
Q

If A & B are mutually exclusive thenP(AuB) =

A

0

41
Q

if you have an experiment that has 4 outcomes or sample points what is the total of all sample points

A

1

42
Q

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

A

.4

the sum of all sample points = 1

43
Q

If A and B are mutually exclusive with P(A)= .3 P(B) = .32, then P(A|B)=

A

0

because if B happens, then A cannot happen

44
Q

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)?

A

P(B) = P(ANB) / P(A)

45
Q

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)?

A

P(AnB) / P(A)

.3/.45

46
Q

Two events A and B. Are they independent or Dependent

P(A| B)=P(A|B’)

A

Independent

47
Q

Two events A and B. Are they dependent or independent

P(B∣A)=P(B∣A′)

A

Independent

48
Q

The example of removing marbles from a bag without replacing them is dependent or independent?

A

Dependent

49
Q

Calculate the Prob of (A and B) for a DEPENDENT event

intersection / multiplication rule

A

P(AnB) = P(B)x P(A|B)

or
P(Anb) = P(A)x P(B|A)

50
Q

Calculate the Prob of A|B) for an independent event

A

P(A|B) = P(A)

51
Q

Calculate the Prob of A|B) for an independent event

A

P(A|B) = P(A)

52
Q

for independent events how do you calculate the P(b)

You know the following:
P(A), P(AandB)

A

P(B) = P(AnB) / P(A)

53
Q

The union of two events with nonzero probabilities can / cannot be

A

mutually exclusive and independent

54
Q

If the prob A and Prob B = P(AnB) then what can be said (independent or dependent)

A

Independent events

class 1 (22 decks)

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