The formula for joint probability is given by:
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A. B. C. D.C
A joint probability takes the form of P(AB) = P(A | B) * P(B). Note that this is just a rearranged form of the formula for conditional probability.
The correct answer for the formula of joint probability is A. P(AB) = P(A | B) * P(B).
To understand this formula, let's break it down step by step:
Joint probability refers to the probability of two events A and B occurring simultaneously.
P(A | B) represents the conditional probability of event A occurring given that event B has already occurred. This can be interpreted as the probability of event A happening "under the condition" that event B has already taken place.
P(B) represents the probability of event B occurring.
Multiplying P(A | B) by P(B) gives us the joint probability P(AB), which is the probability of both events A and B occurring together.
Here's an intuitive way to understand the formula:
Imagine you have a bag of colored marbles. Event A represents picking a red marble from the bag, and event B represents picking a blue marble from the same bag.
P(A | B) represents the probability of picking a red marble (event A) given that you already know a blue marble has been picked (event B). In other words, it is the probability of drawing a red marble from the remaining marbles after a blue marble has been removed.
P(B) represents the probability of picking a blue marble from the bag, which is the initial probability before any marbles are drawn.
P(AB) represents the joint probability of picking both a red marble and a blue marble together.
Using this example, we can see that the formula P(AB) = P(A | B) * P(B) is the correct formula for joint probability.
Therefore, the correct answer is A. P(AB) = P(A | B) * P(B).