A and B are two events. A and B are their complement events, respectively, such that AB and AB are two mutually exclusive and exhaustive events in which the event A can occur. Then which option is correct?

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

Consider the following statements: 1. Two events are mutually exclusive if the occurrence of one event prevents the occurrence of the other. 2. The probability of the union of two mutually exclusive events is the sum of their individual probabilities. 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

Consider the following statements: 1. If A and B are exhaustive events, then their union is the sample space. 2. If A and B are exhaustive events, then their intersection must be an empty event. Which of the above statements is / are correct?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

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 A₁, A₂ . . . . . . . . A_n are 'n' mutually exclusive and exhaustive events and B is a common event, then Baye's theorem deals with

A

P(B/A_i)

B

$$\sum $$P(B $$ \cap $$ A_i)

C

P(A_i $$ \cup $$ B)

D

P(A_i/B)

Which of the following are correct about complementary events? (A) Mutually exclusive (B) Independent (C) Such that their probabilities add up to 1. (D) Collective exhaustive. Choose the most appropriate answer from the options given below:

A

A, B, C only

B

A, B, D only

C

B, C, D only

D

A, C, D only

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)

In a competition A, B and C are participating. The probability that A wins is twice that of B, the probability that B wins is twice that of C. Then the probability that A loses is (A, B and C are mutually exclusive and exhaustive events)

A

4/7

B

3/7

C

2/7

D

1/7

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

A and B are two events. A and B are their complement events, respectively, such that AB and AB are two mutually exclusive and exhaustive events in which the event A can occur. Then which option is correct?

Related Questions