Final answer:
The probabilities of selecting various combinations of marbles from the bag are calculated by multiplying the individual probabilities of drawing each marble, considering that after each draw, the marble is replaced.
Step-by-step explanation:
The probability of selecting different combinations of marbles from the bag can be determined using the basic principles of probability. Since the marbles are replaced after each draw, the number of possible marbles remains consistent, allowing us to use the same probabilities for subsequent draws.
- A) P(both blue): The probability of drawing a blue marble on the first draw times the probability of drawing a blue marble on the second draw. There are 3 blue marbles out of 10 total, so P(blue on 1st draw) = 3/10. Since the marble is replaced, P(blue on 2nd draw) = 3/10 as well. Multiplying these probabilities together gives P(both blue) = (3/10) * (3/10) = 9/100.
- B) P(both red): Similarly, P(red on 1st draw) = 5/10 and P(red on 2nd draw) = 5/10. Multiplying these probabilities gives P(both red) = (5/10) * (5/10) = 25/100.
- C) P(blue then green): P(blue on 1st draw) = 3/10 and P(green on 2nd draw) = 2/10. Thus, P(blue then green) = (3/10) * (2/10) = 6/100.
- D) P(red then blue): P(red on 1st draw) = 5/10 and P(blue on 2nd draw) = 3/10. So, P(red then blue) = (5/10) * (3/10) = 15/100.
- E) P(green then red): P(green on 1st draw) = 2/10 and P(red on 2nd draw) = 5/10. Thus, P(green then red) = (2/10) * (5/10) = 10/100.
- F) P(both green): P(green on 1st draw) = 2/10 and P(green on 2nd draw) also equals 2/10. Multiplying these probabilities yields P(both green) = (2/10) * (2/10) = 4/100.