Select the correct answer from each drop-down menu. A manufacturer tests a certain number of the headsets that are produced each day, with approximately \( 3 \% \) of the headsets found defective. If 280 units of that model are tested, and the manufacturer finds 273 headsets without any defects, there is a defective headset. If the theoretical model is valid, and 1,000 units of that model are tested, the company would expect the empirical probability to \( \square \)

6. Rainy Days A weather forecast system predicts rain using three models: \( M_{1}, M_{2}, M_{3} \). - \( M_{1} \) is used \( 50 \% \) of the time, \( M_{2} 30 \% \), and \( M_{3} 20 \% \). - The probabilities of correctly predicting rain are \( 85 \%, 80 \% \), and \( 90 \% \) for \( M_{1}, M_{2} \), and \( M \) respectively. A random day is selected. - What is the probability that rain is correctly predicted?

If you draw a card from a deck and do not replace it, what type of events does this represent when drawing a second card?

Select the correct answer from each drop-down menu. A manufacturer tests a certain number of the headsets that are produced each day, with approximately \( 3 \% \) of the headsets found defective. If 280 units of that model are tested, and the manufacturer finds 273 headsets without any defects, there is a defective headset. If the theoretical model is valid, and 1,000 units of that model are tested, the company would expect the empirical probability to \( \square \)

6. Rainy Days A weather forecast system predicts rain using three models: \( M_{1}, M_{2}, M_{3} \). - \( M_{1} \) is used \( 50 \% \) of the time, \( M_{2} 30 \% \), and \( M_{3} 20 \% \). - The probabilities of correctly predicting rain are \( 85 \%, 80 \% \), and \( 90 \% \) for \( M_{1}, M_{2} \), and respectively. A random day is selected. - What is the probability that rain is correctly predicted?

You pick a card from a shuffled pack and draw a king. You put it back in the pack, shuffle, and then pick another card. This time you draw a queen. How are the two events of picking a king and picking a queen related? A. dependent B. both dependent and independent C. independent D. neither dependent nor independent