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If A<sub>1</sub>, A<sub>2</sub> . . . . . . . . A<sub>n</sub> are 'n' mutually exclusive and exhaustive events and B is a common event, then Baye's theorem deals with
A
P(B/A<sub>i</sub>)
B
$$\sum $$P(B $$ \cap $$ A<sub>i</sub>)
C
P(A<sub>i</sub> $$ \cup $$ B)
D
P(A<sub>i</sub>/B)
Correct Answer:
P(A<sub>i</sub>/B)
Which of the following statements are true?
1. The classical approach to probability theory requires that the total number of possible outcomes be known or calculated and that each of the outcomes be equally likely.
2. A marginal probability is also known as unconditional probability.
3. For three independent events, the joint probability of the three events, P (ABC) = P (A) × P (B/A) × P (C/AB)
4. Two events are mutually exclusive, exhaustive and equally likely, the probability of either event A or B or both occurring P(A or B) = P(A) + P(B)
A
Both 1 and 3
B
Both 3 and 4
C
1, 2 and 4
D
All of the above
The following are the two statements relating to the theory of probability. Indicate the statements being correct or incorrect.
Statement I The probability of the joint occurrence of independent events A and B is equal to the probability of event A multiplied by the probability of event B or
vice-versa
.
Statement II The probability of the joint occurrence of independent event A and dependent event B is equal to the probability of event A multiplied by the conditionalprobability of event B when event A has occurredor
vice-versa
.
A
Both statements are correct
B
Both statements are incorrect
C
Statement I is correct while Statement II is incorrect
D
Statement I is incorrect while Statement II is correct
Type of distribution, which describes whether events to be occurred are mutually exclusive or collectively exhaustive can be classified as
A
mutual distribution
B
probability distribution
C
collective distribution
D
marginal distribution
If A and B are two mutually exclusive events, then probability that either of the two events will appear is the sum of their
A
Individual probabilities
B
likely events
C
entire population
D
None of these
Additional theorem states that if two events A and B are mutually exclusive the probability of occurrence of either A and B is given by
A
P(B) × P(A)
B
P(A) - P(B)
C
P(A) + P(B)
D
None of these
Addition theorem states that if two events A and B are mutually exclusive the probability of occurrence of either A or B is given by
A
P(A) + P(B)
B
P(A $$ \cup $$ B) + P(A $$ \cap $$ B)
C
P(A) - P(B)
D
None of these
The . . . . . . . . that one of the several mutually exclusive events X
1
, X
2
, X
3
, . . . . . . . . , X
n
; shall happen is the sum of the probabilities of the individual events.
A
regression analysis
B
correlation analysis
C
probability
D
error
Bayes theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event.
A
TRUE
B
FALSE
Bayes' theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event.
A
TRUE
B
FALSE
Arrange the following steps in sequence in order to calculate the probability of an event through Naïve Bayes classifier. I. Find the likelihood probability with each attribute for each class. II. Calculate the prior probability for given class labels. III. Put these values in Bayes formula and calculate posterior probability. IV. See which class has a higher probability, given the input belongs to the higher probability class.
A
I → II → III → IV
B
II → I → III → IV
C
III → II → I → IV
D
II → III → I → IV