PROBABILITY THEORY AND THE BINOMIAL DISTRIBUTION Flashcards
Rationale for studying probability
Often we do not have information about a population. The theory of probability enables us to ____________ about populations.
draw inferences
Medicine and Public Health are an exact science
T/F
F
Medicine and Public Health are not an exact sciences
Probability is central to decision making in Medicine and Public Health
T/F
T
Types of probability
There are two types of probability:
–_________
–___________
Subjective
Empirical
Types of probability
– Empirical:
•____________ outcomes
•_______________of occurence
equally likely
relative frequency
Types of probability
Subjective:
_______________________________ about a person, an event or phenomenon
Empirical:
The _________________ of an event which can be __________.
One’s degree of confidence or doubt
likelihood of occurrence ; quantified
Empirical probability is not a function of one’s belief or doubt
T/F
T
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)
frequency
proportion of times in which the event occurs in the long run
P(A) = nA /N
Where
N = ____________
nA = ____________________
number of trials
number of times that A occurs
If we toss a coin 100 times, and we have heads 50 times,
we speak of P (H) = ___/___ =____
50/100 =1/2.
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 ______
0.15
70/100 or 0.7
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 ————-
six
one in six.
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) = __/___
1/6
one
six
1/6
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= __/____
1/2.
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 ______.
not equally likely
they (outcomes) are
observations and experience
theory
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
certain not to occur
certain to occur
expected to occur with 50% certainty
likely
Laws of Probability
Addition Law: If two or more events are mutually exclusive, the occurrence of one or the other is the __________
sum of their individual probabilities
Laws of Probability
Addition Law:
P (A or B) = _________
P (A or B or C)= ____________
P(A) + P(B)
P(A)+ P(B)+P(C)
Addition Law
The probability of getting a 3 or 5 in a toss of die is _____ + _____ =____ = ___
1/6; 1/6
2/6; 1/3
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 ______ + _____ = ____
1⁄2
1⁄2
1⁄2 + 1⁄2
1
Multiplication Law
Used in ___________ events, where One outcome ______________________
Independent
does not depend on (or is not influenced by) the other
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
product
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 _________ = _____
1/6
1/6.
1/6 X 1/6
1/36
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 = __________= _____
1⁄2
1⁄2
1⁄2 X 1⁄2
1/4
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?
__________ = _____
0.80 X 0.1
0.08
the laws and properties of
probability apply to both relatively frequency and the equally likely approaches in different ways
T/F
F
Note that the laws and properties of
probability apply to both relatively frequency and the equally likely approaches in the same way.
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 ________________
arrangement
a particular order
Permutation formula
Selection and arrangement
NPr = _____________
3P2 = __________ = ___
N! /(N-r)!
3! /(3-2)!
6
Combination
Selections without __________
regard to order
Formula
Permutation: _____= ________
Combination: _______= ______
NPr = N! /(N-r)!
NCx =N!/(N-x)!x!
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?
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
In general: p(X) =______ times ____ Times —————
NCx
P^x
(1-p)^N-x
Binomial Distribution
Arises when there are __________ in any trial (____________________)
two possible outcomes
“success” and “failure”
In Binomial Distribution
Each outcome is independent of the other in successive trials
T/F
T
Each outcome is independent of the other in successive trials
In binomial distribution
The probability for a particular outcome is constant in repeated trials
T/F
T
