What is the conditional probability of an event and how does it differ from the regular probability of an event occurring?
1 Answer
A conditional probability has a new, but smaller sample space compared to the original probabilty
Explanation:
It is best explained with an example ...
A die has 6 possible outcomes, so if you throw the die the results will be one of the following from the sample space:
6-sided die:
Now, let's condition the probability with the following given piece of information: The result is odd .
Given the toss of the die is odd, the new, but smaller sample space is:
6-sided die, given it is odd:
Under the first scenario, the probability of rolling a 3 is:
Under the second conditional scenario, the probability of rolling a 3 is:
In summary, under the first scenario, we divided by the sample space of 6 whereas under the conditional probability we had only 3 in the sample space. This will make a big difference in the probability of rolling a 3 as shown above.
Hope this helped you understand the difference!
