Statistics Probability

An event must be independent of its complement.

false

If A and B are mutually exclusive, then and must be also mutually exclusive

false

If two events are collectively exhaustive they must also be mutually exclusive.

false

If two events are mutually exclusive they must also be collectively exhaustive.

false

If two events are mutually exclusive they must also be independent.

false

The individual probabilities of a pair of events cannot sum more than 1.

false

The probability of the intersection of two events cannot exceed the product of their individual probabilities

false

An event and its complement are mutually exclusive.

true

If an event and its complement are equally likely to occur, the probability of that event must be 0.5.

true

The complement of the union of two events is the intersection of their complements.

true

The conditional probability of A given B must be at least as large as the probability of the intersection of both events.

true

The probability of the intersection of two events cannot be greater than either of their individual proba- bilities.

true

The probability of the union of two events cannot be less than the probability of their intersection.

true

The probability of the union of two events cannot be more than the sum of their individual probabilities.

true

If A and B are two events, the probability of A given B is the same as the probability of B given A if the probability of A is equal to the probability of B.

true (P(A|B) = A ∩ B / B and P(B|A) = A ∩ B/A they, obviously, coincide if P(A) = P(B).