Question

Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

Answer 1

The rule which states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities is "Multiplicative rule".

What is Multiplicative rule?

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

If A and B are dependent events, then the probability of both events occurring simultaneously is given by:

$P(A \cap B)=P(B) \cdot P(A \mid B)$

The likelihood of both events occurring simultaneously in an experiment where A and B are two independent events is given by:

$P(A \cap B)=P(A) \cdot P(B)$

Multiplication Theorem of Probability:

The multiplication guidelines that we use in probability have already been taught to us, including;

$\begin{aligned}&P(A \cap B)=P(A) \times P(B \mid A) \text {; if } P(A) \neq 0 \\&P(A \cap B)=P(B) \times P(A \mid B) \text {; if } P(B) \neq 0\end{aligned}$

Therefore, the relationship between two events is explained by the probability multiplication rule.

Set AB represents the events in which both events A and B have occurred for two events A and B related to a sample space S.

Consequently, (AB) indicates that occurrences A and B happened at the same time. You can write the event AB as AB.

Using the characteristics of conditional probability, the likelihood of event AB is calculated.

To know more about rule of multiplication, here

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