Question

Answer true or false to each statement and explain your answers.

(a) For any two events, the probability that one or the other of the events occurs equals the sum of the two individual probabilities.

(b) For any event, the probability that it occurs equals 1 minus the probability that it does not occur.

Short answer

Part (a) False

Part (b) True

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

Answer true or false to each statement and explain your answers.

(a) For any two events, the probability that one or the other of the events occurs equals the sum of the two individual probabilities.

(b) For any event, the probability that it occurs equals 1 minus the probability that it does not occur.

Part (a) Step 2. State Whether the given statement is true or false.

Given statement: For any two events, the probability that one or the other of the events occurs equals the sum of the two individual probabilities.

The above-given statement is false.

The reason is it only happens in the case of mutually exclusive events.

If the events are mutually exclusive, the likelihood of one or both of them happening equal the total of the two individual probabilities.

Part (b) Step 1. State Whether the given statement is true or false.

Given statement:

For any event, the probability that it occurs equals 1 minus the probability that it does not occur.

The above-given statement is true.

Because it shows the complement rule of probability.