The . . . . . . . . that one of the several mutually exclusive events X1, X2, X3, . . . . . . . . , Xn; shall happen is the sum of the probabilities of the individual events.

The . . . . . . . . that one of the several mutually exclusive events X1, X2, X3, . . . . . . . . , Xn; shall happen is the sum of the probabilities of the individual events.

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)

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 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

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

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

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

In the following passage, some of the words have been left out. Read the passage carefully and select the correct answer for the given blank out of the four alternatives. People may see, and hear, and feel all their lives without ____________ learning the nature of things they see. But reason is the mind's eye, and enables us to see why things are, and when and how events may be made to happen ___________ not to happen. The logician endeavours to ____________ exactly what this reason is which makes the power of men. We all, as I have said, must reason well or ill, but logic is the science of reasoning and enables us to distinguish ______________ the good reasoning which leads to truth, and the bad reasoning which every day betrays people into error _________ misfortune. made to happen ___________ not to happen.

A

or

B

but

C

so

D

at

The probabilities of three mutually exclusive outcomes of an experiment 0.25(1 - x), 0.5(1 - 2x) and 0.25(1 + 4x) respectively. Which of the following holds for the value of x?

A

0.5 ≤ x ≤ 0.5

B

0 ≤ x ≤ 0.5

C

−0.75 ≤ x ≤ 0.25

D

−0.25 ≤ x ≤ 0.5

Given the probabilities P(A) = 0.3 and P(B) = 0.2, what is the probability of the union P(A ? B) if A and B are mutually exclusive? If A and B are independent? If B is a subset of A?

A

0.44, 0.5, 0.2

B

.44, 0.5, 0.3

C

.5, 0.44, 0.2

D

.5, 0.44, 0.3

Given the probabilities P(A) = 0.4 and P(A ? B) = 0.6, what is the probability P(B) if A and B are mutually exclusive? If A and B are independent?

A

0.2, 0.4

B

0.2, 0.33

C

0.33, 0.2

D

0.6, 0.33

The . . . . . . . . that one of the several mutually exclusive events X₁, X₂, X₃, . . . . . . . . , X_n; shall happen is the sum of the probabilities of the individual events.

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