Final answer:
The probabilities for drawing two marbles with replacement from a bag with a mix of colors were recalculated. Correct probabilities are a) 9/100 for two red marbles, b) 1/10 for a blue then a green marble, c) 3/20 for a red then a blue marble, and d) 1/25 for two green marbles.
Step-by-step explanation:
The question deals with the concept of probability, particularly the probability of compound events when drawing marbles with replacement. Each marble drawn is an independent event since the marble is replaced each time, meaning the probability remains the same for each draw.
Let's correct the initial answers given and find the correct probabilities for each compound event mentioned:
- a) P(red, red): Since there are 3 red marbles out of a total of 10, the probability of drawing a red marble is 3/10. Since the marble is replaced, the probability remains the same for the second draw. Therefore, the probability of drawing two red marbles in a row is (3/10) * (3/10) = 9/100.
- b) P(blue, green): The probability of drawing a blue marble is 5/10, and the probability of drawing a green marble on the second draw is 2/10. Thus, P(blue, green) = (5/10) * (2/10) = 10/100 = 1/10.
- c) P(red, blue): The probability of drawing a red marble is 3/10 and drawing a blue marble next is 5/10. P(red, blue) = (3/10) * (5/10) = 15/100 = 3/20.
- d) P(green, green): With the probability of drawing a green marble being 2/10, the probability of drawing two green marbles is (2/10) * (2/10) = 4/100 = 1/25.
The initial answers provided were incorrect, and here we've calculated the correct probabilities for each of the compound events.