J and K are independent events. P(J | K) = 0.3. Find P(J) to one decimal place.

Since \( J \) and \( K \) are independent events, the conditional probability \( P(J | K) \) is equal to \( P(J) \). By the definition of independence, we have:

\[
P(J | K) = P(J)
\]

Given that \( P(J | K) = 0.3 \), it follows that:

\[
P(J) = 0.3
\]

So, the probability \( P(J) \) is 0.3, rounded to one decimal place.

Would you like further clarification or additional details?

Here are some related questions to expand your understanding:

1. What is the formula for conditional probability in general cases?
2. How do you calculate the probability of two independent events happening together?
3. If \( P(K) = 0.5 \), what is \( P(J \cap K) \)?
4. How would the problem change if \( J \) and \( K \) were not independent?
5. Can two events be independent if \( P(J | K) \neq P(J) \)?

**Tip:** Independence of events means that the occurrence of one event does not affect the probability of the other event occurring.

Learn how to find the probability P(J) when J and K are independent events, and P(J | K) is given as 0.3. This problem covers key probability concepts such as independent events and conditional probability, suitable for high school students in Grades 10-12.

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