To determine which events have a probability greater than one-fifth (or 0.2), we need to calculate the probability for each of the events listed.
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Choosing 1 blue marble:
- Total marbles = 2 (blue) + 3 (red) + 5 (white) = 10.
- Probability = Number of blue marbles / Total marbles = 2/10 = 1/5 = 0.2.
- This probability is not greater than one-fifth.
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Choosing 1 red marble:
- Probability = Number of red marbles / Total marbles = 3/10 = 0.3.
- This probability is greater than one-fifth.
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Choosing 1 red marble, not replacing it, and then choosing a blue marble:
- Probability of first choosing a red marble = 3/10.
- After choosing a red marble, there are now 9 marbles left (2 blue, 2 red, 5 white).
- Probability of then choosing a blue marble = 2/9.
- Total probability = (3/10) * (2/9) = 6/90 = 1/15 = 0.0667.
- This probability is not greater than one-fifth.
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Choosing 1 white marble, replacing it, and choosing another white marble:
- Probability of choosing the first white marble = 5/10 = 1/2.
- Since the marble is replaced, the probability of choosing a second white marble is also 1/2.
- Total probability = (1/2) * (1/2) = 1/4 = 0.25.
- This probability is greater than one-fifth.
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Choosing 1 white marble:
- Probability = Number of white marbles / Total marbles = 5/10 = 1/2 = 0.5.
- This probability is greater than one-fifth.
Based on this analysis, the events that have a probability greater than one-fifth are:
- Choosing 1 red marble.
- Choosing 1 white marble, replacing it, and choosing another white marble.
- Choosing 1 white marble.
Thus, the three options that have a probability greater than one-fifth are:
- Choosing 1 red marble
- Choosing 1 white marble, replacing it, and choosing another white marble
- Choosing 1 white marble