The sample space of an experiment is S={1, 2, 3, 4, 5}. If each outcome is equally likely to occur
, the probability of each outcome is 1/5 or 0.2.
For example, the probability of rolling a 3 with a fair six-sided die is also 1/6 or approximately 0.167.
To calculate the probability of an event A, which is a subset of the sample space S, we add up the probabilities of all outcomes in A:
P(A) = sum of probabilities of all outcomes in A
For example, if event A is "rolling an odd number", then A={1,3,5} and
P(A) = P(1) + P(3) + P(5)
= 0.2 + 0.2 + 0.2
= 0.6
So the probability of rolling an odd number in this experiment is 0.6 or 60%.
If each outcome is equally likely to occur, the probability of an event A occurring can be calculated using the formula:
P(A) = Number of outcomes in A / Total number of outcomes
Let's consider an example to illustrate this concept.
Example:
The sample space of an experiment is S = {1, 2, 3, 4, 5}.
We want to find the probability of rolling an even number.
Step 1: Determine the event A.
In this case, event A is rolling an even number.
Step 2: Count the number of outcomes in A.
The even numbers in the sample space S are {2, 4}.
So, there are 2 outcomes in A.
Step 3: Count the total number of outcomes.
The total number of outcomes in the sample space S is 5.
Step 4: Calculate the probability of event A.
Using the formula:
P(A) = Number of outcomes in A / Total number of outcomes
P(A) = 2 / 5
Therefore, the probability of rolling an even number in this example is 2/5 or 0.4.
If each outcome in the sample space is equally likely to occur, it means that the probability of each outcome is the same.
To find the probability of an event, we divide the number of favorable outcomes by the number of possible outcomes.
In this case, the number of possible outcomes is the total number of elements in the sample space, which is 5 (S={1, 2, 3, 4, 5}).
Let's say we want to find the probability of getting an even number. The favorable outcomes would be the numbers 2 and 4 since they are the only even numbers in the sample space. Therefore, the number of favorable outcomes is 2.
So, the probability of getting an even number is 2/5 or 0.4.