Answer :
Final answer:
The probability that the 2 counters will be the same color is 1/4. The probability that the 2 counters will be red is 2/9.
Explanation:
To find the probability that the 2 counters will be the same color, we need to consider the possible combinations of counters from both bags.
A. The probability that the 2 counters will be the same color:
- Count the number of counters of each color from both bags. The 1st bag has 2 red counters and 1 blue counter, while the 2nd bag has 1 red counter and 1 blue counter.
- Calculate the probability of getting 2 red counters:
- Probability of getting a red counter from the 1st bag: 2/3
- Probability of getting a red counter from the 2nd bag: 1/4
- Total probability = (2/3) * (1/4) = 2/12 = 1/6
- Probability of getting a blue counter from the 1st bag: 1/3
- Probability of getting a blue counter from the 2nd bag: 1/4
- Total probability = (1/3) * (1/4) = 1/12
- Final probability = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4
B. The probability that the 2 counters will be red:
- Count the number of red counters from both bags. The 1st bag has 2 red counters and the 2nd bag has 1 red counter.
- Calculate the total number of counters from both bags:
- Total number of counters = number of counters in the 1st bag + number of counters in the 2nd bag = 2 + 1 = 3
- Probability of getting a red counter from the 1st bag: 2/3
- Probability of getting a red counter from the 2nd bag: 1/3
- Total probability = (2/3) * (1/3) = 2/9
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