Answer: You are in deed altering the sample space, leading to a change in probabilities and outcomes. So true :)
Step-by-step explanation:
When we add a condition to a probability, changing from a simple probability of P(A) to a conditional probability of P(A|B), we are indeed changing the sample space. This statement is True.
Here's a step-by-step explanation:
1. Simple Probability (P(A)):
- When we calculate the simple probability P(A), we are looking at the likelihood of event A occurring without any conditions or additional information.
- The sample space for calculating P(A) includes all possible outcomes of the experiment.
2. Conditional Probability (P(A|B)):
- When we calculate the conditional probability P(A|B), we are considering the probability of event A occurring given that event B has already occurred.
- The sample space for calculating P(A|B) is restricted to the outcomes where event B has occurred, which changes the perspective and alters the probabilities.
3. Example:
- Suppose we have a deck of cards, and event A is drawing a red card, while event B is drawing a heart.
- P(A) would be the probability of drawing a red card, which includes both hearts and diamonds.
- P(A|B) would be the probability of drawing a red card given that we already know a heart has been drawn. In this case, the sample space is reduced to just the hearts, changing the probability.
Therefore, when we move from a simple probability (P(A)) to a conditional probability (P(A|B)), we are indeed altering the sample space, leading to a change in probabilities and outcomes.