If two events A and B are dependent, the conditional probability of A given B, i.e., P (A/B) is calculated as:

For realizing a binary half-subtractor having two inputs A and B, the current set of logical expression for the outputs D (A minus B) and X (borrow) are 1. The difference output D = A̅B + AB̅ 2. The borrow output B = AB̅ Which of the above statements is/are correct?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

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

If two events A and B are dependent, the conditional probability of B given A, i.e., P(^B/_A) is calculated as

A

^P(AB)/_P(B)

B

^P(A)/_(B)

C

^P(A)/_P(B)

D

^P(A)/_P(A)

If two events A and B are dependent the conditional probability of A, given B, i.e., $${\text{P}}\left( {\frac{{\text{A}}}{{\text{B}}}} \right)$$ is calculated as

A

$$\frac{{{\text{P}}\left( {{\text{AB}}} \right)}}{{{\text{P}}\left( {\text{B}} \right)}}$$

B

$${\text{P}}\left( {\frac{{\text{B}}}{{\text{A}}}} \right)\left( {{\text{AB}}} \right)$$

C

$$\frac{{{\text{P}}\left( {\text{B}} \right)}}{{{\text{P}}\left( {\text{A}} \right)}}$$

D

None of these

For calculating posterior probabilities (conditional probabilities under statistical dependence), the following information is available a) conditional probabilities b) original probability estimates (prior probabilities) of mutually exclusive and collectively exhaustive events c) Arbitrary event with probability

A

a) → b) → d) → c)

B

c) → b) → a) → d)

C

b) → c) → d) → a)

D

b) → a) → d) → c)

Let the events E and F denote the following events E: the sum of numbers on two dies is 8 F: the number on the first die is 3 When two fair dice are rolled, then the conditional probability of E given that F has already occurred is given by ______

A

P(E)

B

P(F|E)

C

P(F)

D

P(E|F)

Consider the relational schema given below, where eId of the relation dependent is a foreign key referring to empId of the relation employee. Assume that every employee has at least one associated dependent in the dependent relation. Employee (empId, empName, empAge) Dependent(depId, eId, depName, depAge) Consider the following relational algebra query: ΠempId(employee)-ΠempId (employee⋈(empId = eID)∧(empAge ≤ depAge)dependent) The above query evaluates to the set of empIds of employees whose age is greater than that of

A

some dependent.

B

all dependents

C

some of his/her dependents

D

all of his/her dependents

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

A probability distribution with right skew is shown in the figure.
Probability and Statistics mcq question image

The correct statement for the probability distribution is

A

Mean is equal to mode

B

Mean is greater than median but less than mode

C

Mean is greater than median and mode

D

Mode is greater than median

If two events A and B are dependent, the conditional probability of A given B, i.e., P (A/B) is calculated as:

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