If A and B are two mutually exclusive events, then what is the probability of occurrence of either event A or event B?

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

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

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?

A

P(A) = P(A̅B) + P(AB̅)

B

P(A) = P(AB) + P(AB̅)

C

P(A) = P(A̅) + P(AB̅)

D

P(A) = 1

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

"Two or more events are called mutually exclusive, if the occurrence of anyone of them excludes the occurrence of the other." This statement is given by

A

M. S. Roy

B

Morris Hamburg

C

Murray Spiegel

D

Emile Bovel

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

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)

If A and B are two mutually exclusive events, then what is the probability of occurrence of either event A or event B?

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