What is the probability of the following.(a) An event A that is certain to occur?(b) An event B that is impossible?

To address the question of probability for the defined events, let's examine each event clearly.

(a) Probability of an event A that is certain to occur

1. Understanding Event A: An event is said to be certain if it will definitely happen. This means that there are no conditions under which this event can fail to occur.

2. Probability Definition: The probability of an event $A$ is defined mathematically as: $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

3. Calculating Probability: For a certain event (e.g., rolling a die and getting a number between 1 and 6), the number of favorable outcomes equals the total number of outcomes (6 in this case). Thus, $P(A) = \frac{6}{6} = 1$

(b) Probability of an event B that is impossible

1. Understanding Event B: An event is said to be impossible if there are no possible outcomes for the event to occur. For example, rolling a 7 on a standard die is impossible.

2. Calculating Probability: Following the probability definition, for an impossible event:

   • Number of favorable outcomes = 0
   • Total number of outcomes = 6 (on a die)

   Thus, the probability for an impossible event would be: $P(B) = \frac{0}{6} = 0$

Final Answer

• The probability of an event $A$ that is certain to occur is $P(A) = 1$.
• The probability of an event $B$ that is impossible is $P(B) = 0$.