Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

COMMERS > PROBABILITY THEORY AND THE BINOMIAL DISTRIBUTION > Flashcards

PROBABILITY THEORY AND THE BINOMIAL DISTRIBUTION Flashcards

1
Q

Rationale for studying probability

Often we do not have information about a population. The theory of probability enables us to ____________ about populations.

A

draw inferences

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Medicine and Public Health are an exact science

T/F

A

F

Medicine and Public Health are not an exact sciences

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Probability is central to decision making in Medicine and Public Health

T/F

A

T

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Types of probability

There are two types of probability:
–_________
–___________

A

Subjective

Empirical

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Types of probability

– Empirical:
•____________ outcomes

•_______________of occurence

A

equally likely

relative frequency

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Types of probability

Subjective:
_______________________________ about a person, an event or phenomenon

Empirical:
The _________________ of an event which can be __________.

A

One’s degree of confidence or doubt

likelihood of occurrence ; quantified

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Empirical probability is not a function of one’s belief or doubt

T/F

A

T

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Definition of Probability
There are many definitions of probability but we shall use the _________ definition.

The probability that an event will occur under a given circumstance is defined as the _________________________ ( in repeated trials)

A

frequency

proportion of times in which the event occurs in the long run

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

P(A) = nA /N

Where
N = ____________
nA = ____________________

A

number of trials

number of times that A occurs

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

If we toss a coin 100 times, and we have heads 50 times,

we speak of P (H) = ___/___ =____

A

50/100 =1/2.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Frequency definition
If 15 out of 100 patients admitted to an intensive care unit die before discharge, then we can speak of the probability of dying as being ______

If 100 patients are given a particular treatment and 70 recover, we speak of the probability of recovery as ___/____ or ______

A

0.15

70/100 or 0.7

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Equally likely outcomes

Probability can also be defined in terms of equally likely outcomes.

In the toss of a dice, there are ____ equally likely outcomes, so the probability of any number appearing in any toss is ————-

A

six

one in six.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Probability of having the number 4 as an outcome in a single toss is ____, i.e. ___ outcome out of the ____ equally likely outcomes.

P (4) = __/___

A

1/6

one

six

1/6

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

In the toss of a coin, there two equally likely outcomes, a head or a tail.

So the probability of having a “head” in a single toss= __/____

A

1/2.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Why focus on the relative frequency definition?

Many outcomes in real life are ________
We do not even know whether ________
Relative frequency is based on ________ and _______ rather than on ______.

A

not equally likely

they (outcomes) are

observations and experience

theory

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Probability of 0 = event is ___________
Probability of 1= event is —————
Probability of 0.5 = event is _________________

The closer the value to 1 the more
________ is the event t

A

certain not to occur

certain to occur

expected to occur with 50% certainty

likely

17
Q

Laws of Probability

Addition Law: If two or more events are mutually exclusive, the occurrence of one or the other is the __________

A

sum of their individual probabilities

18
Q

Laws of Probability

Addition Law:

P (A or B) = _________
P (A or B or C)= ____________

A

P(A) + P(B)

P(A)+ P(B)+P(C)

19
Q

Addition Law
The probability of getting a 3 or 5 in a toss of die is _____ + _____ =____ = ___

A

1/6; 1/6

2/6; 1/3

20
Q

Addition law

If the probability of a having a boy as first child is ____.
The probability of having a girl is also _______

the probability of having a boy or girl is ______ + _____ = ____

A

1⁄2

1⁄2

1⁄2 + 1⁄2

1

21
Q

Multiplication Law

Used in ___________ events, where One outcome ______________________

A

Independent

does not depend on (or is not influenced by) the other

22
Q

When two (say A and B) or more events are independent, the probability of joint occurrence (eg the occurrence of A and B) is the _______ of the individual probabilities

A

product

23
Q

Multiplication Law

The probability of getting a four in a single throw of a dice is _______ . The probability of getting another four in the next throw is ______

The probability of getting two “fours” in two consecutive throws is _________ = _____

A

1/6

1/6.

1/6 X 1/6

1/36

24
Q

Multiplication Law
If the probability of a having a boy as first child is _______, and the probability of having a boy as a second child is also ______ the probability of having two boys consecutively = __________= _____

A

1⁄2

1⁄2

1⁄2 X 1⁄2

1/4

25
Q

Multiplication Law

In a population, the prevalence of hypertension is 10% and the proportion of people with blood group O is 80%. If we randomly select an individual from this population, what is the probability that s/he is hypertensive with blood group O?
__________ = _____

A

0.80 X 0.1

0.08

26
Q

the laws and properties of
probability apply to both relatively frequency and the equally likely approaches in different ways

T/F

A

F

Note that the laws and properties of
probability apply to both relatively frequency and the equally likely approaches in the same way.

27
Q

Permutations and Combinations

A knowledge of permutations and combinations is useful in dealing with many problems involving probabilities.
Permutation refers to the ________ of events/objects in ________________

A

arrangement

a particular order

28
Q

Permutation formula

Selection and arrangement

NPr = _____________

3P2 = __________ = ___

A

N! /(N-r)!

3! /(3-2)!

6

29
Q

Combination
Selections without __________

A

regard to order

30
Q

Formula

Permutation: _____= ________

Combination: _______= ______

A

NPr = N! /(N-r)!

NCx =N!/(N-x)!x!

31
Q

The probability of success in a particular therapy is 0.7.
Four patients with the condition are subjected to the therapy, what is the probability that two of them will be successfully treated?

A

0.7 x 0.7 x 0.3 x 0.3 = 0.0441

Success x Success x Fail x Fail

Times 6 because it says any 2 , not first 2

= 0.0441 x 6= 2646

32
Q

In general: p(X) =______ times ____ Times —————

A

NCx

P^x

(1-p)^N-x

33
Q

Binomial Distribution
 Arises when there are __________ in any trial (____________________)

A

two possible outcomes

“success” and “failure”

34
Q

In Binomial Distribution

Each outcome is independent of the other in successive trials

T/F

A

T

Each outcome is independent of the other in successive trials

35
Q

In binomial distribution

The probability for a particular outcome is constant in repeated trials

T/F

A

T

COMMERS (11 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions