What Multiplication rule is
The multiplication rule states that the probability of two independent events occurring simultaneously is the product of their individual probabilities. This means that if two events, A and B, are independent, then the probability of both occurring is:
P(A and B) = P(A) x P(B)
The multiplication rule can be used to calculate the probability of independent events occurring in a sequence. For example, if the probability of event A occurring is 0.4 and the probability of event B occurring is 0.6, the probability of both A and B occurring is 0.4 x 0.6 = 0.24.
Steps for the multiplication rule:
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Determine the probability of each event.
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Multiply the probabilities of each event together.
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The result is the probability of both events occurring simultaneously.
Examples
Example 1: In a survey of 100 people, if 40 individuals have a certain trait, then it can be assumed that 4 out of every 10 people have that trait, using the multiplication rule.
Example 2: If a sample of 1000 people is taken from a population of 500,000 and it is found that 10% of the sample have a certain characteristic, the multiplication rule can be used to estimate that 50,000 of the population of 500,000 have the characteristic.