Final answer:
The probability that someone knows Java, given that they also know Python, is approximately 83.3%, calculated by dividing the probability of knowing both languages by the probability of knowing Python. The closest option is D) 0.50
Step-by-step explanation:
To calculate the probability that someone knows Java, given that they know Python as well, we can use Bayes' theorem or directly approach the problem with the understanding of conditional probability.
According to the question, 70% of the employees know Java, which is represented as P(J) = 0.70, and 60% know Python, represented as P(P) = 0.60. Moreover, 50% know both Java and Python, represented as P(J ∩ P) = 0.50.
The probability that someone knows Java given that they know Python can be found using the formula for conditional probability:
P(J | P) = P(J ∩ P) / P(P)
Substituting the given probabilities:
P(J | P) = 0.50 / 0.60
P(J | P) = 0.833...
This means that the probability is approximately 83.3%, which is not one of the answer choices provided. However, since this is a high probability, it suggests that there might be a miscalculation or a misunderstanding in the provided answer choices. The closest answer choice is option (d) 0.50, yet it does not accurately represent the calculated probability.