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Answer :
To find the probability that Caitlin randomly picks a yellow or green counter, we can follow these steps:
1. Determine the total number of counters in the bag.
There are 12 counters in total.
2. Identify the number of yellow counters.
There are 2 yellow counters.
3. Calculate the number of green counters.
We know:
- 3 counters are red.
- 1 counter is blue.
- 2 counters are yellow.
The rest must be green. To find the number of green counters:
[tex]\[
\text{Total counters} - (\text{red} + \text{blue} + \text{yellow}) = 12 - (3 + 1 + 2) = 12 - 6 = 6
\][/tex]
So, there are 6 green counters.
4. Calculate the probability of picking a yellow or green counter.
There are 2 yellow and 6 green counters. Therefore, the total number of yellow or green counters is:
[tex]\[
2 + 6 = 8
\][/tex]
5. Find the probability.
The probability of picking a yellow or green counter from the total of 12 counters is:
[tex]\[
\frac{8}{12} = \frac{2}{3}
\][/tex]
Therefore, the probability that Caitlin picks a yellow or green counter is [tex]\(\frac{2}{3}\)[/tex].
1. Determine the total number of counters in the bag.
There are 12 counters in total.
2. Identify the number of yellow counters.
There are 2 yellow counters.
3. Calculate the number of green counters.
We know:
- 3 counters are red.
- 1 counter is blue.
- 2 counters are yellow.
The rest must be green. To find the number of green counters:
[tex]\[
\text{Total counters} - (\text{red} + \text{blue} + \text{yellow}) = 12 - (3 + 1 + 2) = 12 - 6 = 6
\][/tex]
So, there are 6 green counters.
4. Calculate the probability of picking a yellow or green counter.
There are 2 yellow and 6 green counters. Therefore, the total number of yellow or green counters is:
[tex]\[
2 + 6 = 8
\][/tex]
5. Find the probability.
The probability of picking a yellow or green counter from the total of 12 counters is:
[tex]\[
\frac{8}{12} = \frac{2}{3}
\][/tex]
Therefore, the probability that Caitlin picks a yellow or green counter is [tex]\(\frac{2}{3}\)[/tex].
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