Final answer:
C) 0.7 The question seems to contain a typo or misunderstanding, as P(J)P(J) would require the individual probability of J. Without it, we cannot determine the exact value.
Step-by-step explanation:
The correct answer is option B) 0.6. Since J and K are independent events, the probability of both J and K occurring, which is represented as P(JK), is the product of their individual probabilities. This means that P(JK) = P(J)P(K). You have been provided with P(JK) = 0.6 but not the individual probabilities for J and K.
However, to calculate P(J)P(J), you would simply square the probability of J, which is not possible without the individual probability of J. Therefore, it looks like there might be a typo or misunderstanding in the question. Without the individual probabilities of J and K, we cannot exactly determine P(J)P(J).
Since J and K are independent events, the probability of both events happening (P(JK)) is equal to the product of their individual probabilities (P(J) and P(K)). In this case, P(JK) = P(J)P(K), so we have 0.6 = P(J)(0.3). Solving for P(J), we find P(J) = 0.6/0.3 = 2/3.
Now, to find P(J)P(J), we simply square the probability of J. Therefore, P(J)P(J) = (2/3)(2/3) = 4/9 ≈ 0.444. However, none of the given options match this value, so it seems there may be an error in the answer choices provided.