Answer :
Sure! Let's work through this step-by-step.
Part (a):
1. Identify the number of each type of counter:
- Red counters: 5
- Blue counters: 6
- Green counters: 1
2. Find the total number of counters in the bag:
- Total counters = 5 (red) + 6 (blue) + 1 (green) = 12 counters
3. Find the probability of taking a counter that is not red:
- Counters that are not red include blue and green counters.
- Total non-red counters = 6 (blue) + 1 (green) = 7 non-red counters
4. Calculate the probability:
- Probability of not picking a red counter = Number of non-red counters / Total counters
- Probability = 7 / 12 ≈ 0.583 (or 58.3%)
Part (b):
1. We know that the probability of taking a red counter is now [tex]\(\frac{1}{3}\)[/tex]:
2. Calculate the new total number of counters in the bag:
- If the probability of picking a red counter is [tex]\(\frac{1}{3}\)[/tex], then:
- [tex]\[ \frac{Number \ of \ red \ counters}{Total \ number \ of \ counters} = \frac{1}{3} \][/tex]
- [tex]\[\frac{5}{Total \ number \ of \ counters} = \frac{1}{3} \][/tex]
- Solve for Total number of counters: Total number of counters = [tex]\(\frac{5}{\frac{1}{3}}\)[/tex] = 15
3. Determine how many green counters are now in the bag:
- We know there are still 5 red counters and 6 blue counters.
- Total counters now are 15.
- Number of green counters now = Total counters - (Red counters + Blue counters)
- Number of green counters now = 15 - (5 + 6) = 4 green counters
Therefore, in the end, the probability of not choosing a red counter is 0.583, and there are now 4 green counters in the bag.
Part (a):
1. Identify the number of each type of counter:
- Red counters: 5
- Blue counters: 6
- Green counters: 1
2. Find the total number of counters in the bag:
- Total counters = 5 (red) + 6 (blue) + 1 (green) = 12 counters
3. Find the probability of taking a counter that is not red:
- Counters that are not red include blue and green counters.
- Total non-red counters = 6 (blue) + 1 (green) = 7 non-red counters
4. Calculate the probability:
- Probability of not picking a red counter = Number of non-red counters / Total counters
- Probability = 7 / 12 ≈ 0.583 (or 58.3%)
Part (b):
1. We know that the probability of taking a red counter is now [tex]\(\frac{1}{3}\)[/tex]:
2. Calculate the new total number of counters in the bag:
- If the probability of picking a red counter is [tex]\(\frac{1}{3}\)[/tex], then:
- [tex]\[ \frac{Number \ of \ red \ counters}{Total \ number \ of \ counters} = \frac{1}{3} \][/tex]
- [tex]\[\frac{5}{Total \ number \ of \ counters} = \frac{1}{3} \][/tex]
- Solve for Total number of counters: Total number of counters = [tex]\(\frac{5}{\frac{1}{3}}\)[/tex] = 15
3. Determine how many green counters are now in the bag:
- We know there are still 5 red counters and 6 blue counters.
- Total counters now are 15.
- Number of green counters now = Total counters - (Red counters + Blue counters)
- Number of green counters now = 15 - (5 + 6) = 4 green counters
Therefore, in the end, the probability of not choosing a red counter is 0.583, and there are now 4 green counters in the bag.
