Final answer:
a. The probability of selecting two blue marbles is 0.36. b. The probability of selecting at least one red marble is 0.52. c. The probability of selecting a red marble first and then a blue marble is 0.24. d. The probability of selecting a red marble and a blue marble is 0.48.
Step-by-step explanation:
a. To find the probability of selecting two blue marbles, we need to find the probability of selecting a blue marble on the first draw and then another blue marble on the second draw. Since there are 12 blue marbles in the bag, the probability of selecting a blue marble on the first draw is 12/20. After replacing the first marble, there are still 12 blue marbles in the bag, so the probability of selecting a blue marble on the second draw is also 12/20. To find the probability of both events happening, we multiply the probabilities together: (12/20) * (12/20) = 144/400 = 0.36.
b. To find the probability of selecting at least one red marble, we need to find the probability of either selecting one red marble or selecting two red marbles. The probability of selecting one red marble is 8/20, and the probability of selecting two red marbles is (8/20) * (8/20) = 64/400 = 0.16. To find the total probability, we add the probabilities together: 8/20 + 64/400 = 0.52.
c. To find the probability of selecting a red marble first and then a blue marble, we need to find the probability of selecting a red marble on the first draw and then a blue marble on the second draw. The probability of selecting a red marble on the first draw is 8/20. After replacing the first marble, the probability of selecting a blue marble on the second draw is 12/20. To find the probability of both events happening, we multiply the probabilities together: (8/20) * (12/20) = 96/400 = 0.24.
d. To find the probability of selecting a red marble and a blue marble, we need to find the probability of selecting a red marble on the first draw and a blue marble on the second draw, or the probability of selecting a blue marble on the first draw and a red marble on the second draw. These two events are mutually exclusive, so we can add their probabilities together. The probability of selecting a red marble on the first draw and a blue marble on the second draw is (8/20) * (12/20) = 96/400 = 0.24. The probability of selecting a blue marble on the first draw and a red marble on the second draw is (12/20) * (8/20) = 96/400 = 0.24. Adding the probabilities together, we get 0.24 + 0.24 = 0.48.