The set of all possible outcomes of a random experiment is called the ___?

Sample space

True or False: The probability of an impossible event is always greater than 0.

False. The probability of an impossible event is 0.

If two events A and B are independent, then the probability of both events occurring simultaneously is given by ___?

P(A) × P(B)

The probability of obtaining exactly r successes in n independent trials follows the formula ___?

P(r) = C(n, r) * p^r * (1-p)^(n-r)

An event that is represented by the empty set is called a ___ event.

Impossible event

If two events A and B are mutually exclusive, then P(A ∩ B) is equal to ___?

0

The probability of at least one event occurring in n independent trials is given by ___?

1 - (1 - p)^n, where p is the probability of success in a single trial.

True or False: The sum of probabilities of all mutually exclusive events in a sample space is always less than 1.

False. The sum of probabilities of all mutually exclusive events in a sample space is always 1.

The occurrence of event E implies the occurrence of event F can be expressed as ___?

P(E | F) = P(E ∩ F) / P(F)

The odds in favor of an event E occurring is given by ___?

P(E) / (1 - P(E))

If events E1, E2, ..., En are mutually exclusive and exhaustive, then the probability of an event A can be calculated using ___?

P(A) = Σ P(Ei) * P(A | Ei) for i = 1 to n

The formula for conditional probability is given by ___?

P(E | F) = P(E ∩ F) / P(F), provided P(F) > 0.

The mean of a binomial distribution with n trials and probability of success p is given by ___?

Np

In a random experiment, if the outcome cannot be predicted with certainty, it is called a ___ experiment.

Random

For any event E, the probability of its complement is given by ___?

P(E') = 1 - P(E)