19. There are 12 yellow, 5 blue, 14 red and 9 green marbles in a bag. A marble is chosen at random, replaced, then another marble is chosen. Find the probability of choosing a blue then not blue. \( P \) (blue, then not blue)

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

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?

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 stay the same increase

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?

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?