Answer :
- The probability of the counter not being blue is 0.7.
- The number of green counters is 45.
Given Information:
- The bag contains blue, green, red, and yellow counters.
- Total counters = 100
- Number of blue counters = 30
- The ratio of blue to green counters is 2:3
Part (a): Probability that the counter is not blue
Find the number of counters that are not blue:
Total counters - Blue counters
= 100 - 30
= 70
Probability formula:
Probability = (Number of not blue counters) / (Total counters)
= 70 / 100
= 0.7
The probability of not picking a blue counter is 0.7.
Part (b): Finding the number of green counters
Let the number of green counters be G.
The ratio of blue to green is 2:3, so we set up a proportion:
30 / G = 2 / 3
30 × 3 = 2 × G
90 = 2G
Solve for G:
G = 90 / 2
G = 45
The number of green counters is 45.
Sure! Let's go through the solution step by step.
### (a) Finding the probability that the counter is not blue:
1. Total number of counters in the bag:
We know from the problem that there are a total of 100 counters in the bag.
2. Number of blue counters:
The table tells us there are 30 blue counters.
3. Number of counters that are not blue:
To find how many counters are not blue, subtract the number of blue counters from the total number of counters:
[tex]\[ \text{Not blue counters} = \text{Total counters} - \text{Blue counters} = 100 - 30 = 70 \][/tex]
4. Probability that the counter is not blue:
Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. So the probability that a counter taken at random is not blue is:
[tex]\[ \text{Probability not blue} = \frac{\text{Not blue counters}}{\text{Total counters}} = \frac{70}{100} = 0.7 \][/tex]
### (b) Working out the number of green counters:
1. Ratio of blue counters to green counters:
We are told the ratio of blue counters to green counters is 2:3.
2. Using the ratio to find the number of green counters:
The given ratio can be written as:
[tex]\[ \frac{\text{Blue counters}}{\text{Green counters}} = \frac{2}{3} \][/tex]
3. Calculate the number of green counters:
Rearrange the ratio equation to solve for green counters:
[tex]\[ \text{Green counters} = \frac{3}{2} \times \text{Blue counters} \][/tex]
Substitute the number of blue counters:
[tex]\[ \text{Green counters} = \frac{3}{2} \times 30 = 45 \][/tex]
Therefore, the probability that a randomly selected counter is not blue is 0.7, and there are 45 green counters in the bag.
### (a) Finding the probability that the counter is not blue:
1. Total number of counters in the bag:
We know from the problem that there are a total of 100 counters in the bag.
2. Number of blue counters:
The table tells us there are 30 blue counters.
3. Number of counters that are not blue:
To find how many counters are not blue, subtract the number of blue counters from the total number of counters:
[tex]\[ \text{Not blue counters} = \text{Total counters} - \text{Blue counters} = 100 - 30 = 70 \][/tex]
4. Probability that the counter is not blue:
Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. So the probability that a counter taken at random is not blue is:
[tex]\[ \text{Probability not blue} = \frac{\text{Not blue counters}}{\text{Total counters}} = \frac{70}{100} = 0.7 \][/tex]
### (b) Working out the number of green counters:
1. Ratio of blue counters to green counters:
We are told the ratio of blue counters to green counters is 2:3.
2. Using the ratio to find the number of green counters:
The given ratio can be written as:
[tex]\[ \frac{\text{Blue counters}}{\text{Green counters}} = \frac{2}{3} \][/tex]
3. Calculate the number of green counters:
Rearrange the ratio equation to solve for green counters:
[tex]\[ \text{Green counters} = \frac{3}{2} \times \text{Blue counters} \][/tex]
Substitute the number of blue counters:
[tex]\[ \text{Green counters} = \frac{3}{2} \times 30 = 45 \][/tex]
Therefore, the probability that a randomly selected counter is not blue is 0.7, and there are 45 green counters in the bag.
