Which of the following defines the probability of an event A, or P(A)?
The probability of A equals 0.50.
The probability of A equals the number of possible outcomes in the sample space divided by the number of outcomes favorable to A.
The probability of A equals the number of outcomes favorable to A divided by the number of possible outcomes in the sample space.
The probability of A equals the number of outcomes favorable to A.
the probability of A equals the the number of favorable outcome to A divided by the number of possible out comes in the sample space
The probability of A equals the number of outcomes favorable to A divided by the number of possible outcomes in the sample space.
The first choice gives a specific probability, but does not define it.
Well, if A is as likely as me catching a pie in my face, then the probability of A equals 0.50. But in a more serious note, the correct definition of the probability of an event A, or P(A), is that it equals the number of outcomes favorable to A divided by the number of possible outcomes in the sample space. So, option C is the winner here!
The correct answer is: The probability of A equals the number of outcomes favorable to A divided by the number of possible outcomes in the sample space.
To understand why this is the correct definition, let's break down the components of the answer:
1. Outcomes favorable to A: These are the outcomes or events that we are interested in, or the outcomes that we consider as successes. For example, if event A is rolling a 6 on a fair six-sided die, then the outcomes favorable to A would be just one, which is rolling a 6.
2. Possible outcomes in the sample space: The sample space refers to the set of all possible outcomes of an experiment. In the case of rolling a fair six-sided die, the possible outcomes in the sample space would be the numbers 1 to 6.
By dividing the number of outcomes favorable to A by the number of possible outcomes in the sample space, we obtain the probability of event A. This formula for calculating probability is based on the assumption of equally likely outcomes.
In the other answer options:
- The first option simply states that the probability of event A is 0.50, which is not a general definition but rather a specific value assigned to the probability.
- The second option incorrectly states that the probability of A equals the number of possible outcomes in the sample space divided by the number of outcomes favorable to A.
- The last option incorrectly states that the probability of A equals the number of outcomes favorable to A, without considering the total number of possible outcomes in the sample space.