Question

using the multiplication rule to determine if events are independent

the probability for event a is 0.3, the probability for event b is 0.5, and the probability of events a and b is 0.25. are the events independent?
because

Explanation:

State the given probabilities

Using the Independent Events and Probability Multiplication Rule knowledge points

$$
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$$

Calculate the product of individual probabilities

Using the Probability Multiplication Rule knowledge point

$$ P(A) \cdot P(B) = 0.3 \cdot 0.5 = 0.15 $$

Compare the product with the joint probability

Using the Independent Events knowledge point

$$
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$$

Answer:

The probability for event A is 0.3, the probability for event B is 0.5, and the probability of events A and B is 0.25. Are the events independent?
<blank>No</blank> because <blank>\(P(A) \cdot P(B)
eq P(A \text{ and } B)\)</blank>