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
