The product rule is a rule in probability and statistics that is used to calculate the probability of two independent events occurring. It states that the probability of the intersection of two independent events is equal to the product of the probabilities of the individual events.
Here is the formula for the product rule:
P(A ∩ B) = P(A) x P(B)
where P(A ∩ B) is the probability of the intersection of events A and B, P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.
Here is an example of how to use the product rule:
Let's say you are playing a game where you flip a coin and roll a die, and you want to know the probability of flipping heads and rolling a 1. If the probability of flipping heads is 50% and the probability of rolling a 1 is 1/6, the probability of both events occurring is 50% x 1/6 = 8.3%.
The product rule is important in probability and statistics because it allows us to calculate the probability of two independent events occurring, and to make more informed decisions based on the likelihood of different outcomes.
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