Question

I’m not sure how you would show the probability that the counter is yellow or green 2/3

Answer 1

`(2)/(3)`

Explanation:

The probability of an event occurring is defined as:

`P = \frac{\#\text{ desired outcomes}}{\#\text{ total outcomes}}`

In this case, the desired outcomes are when the counter pulled at random from a bag is green or yellow.

Since only one counter is being pulled, the number of desired outcomes is the sum of the number of yellow counters and green counters.

First, we need to calculate the number of green counters:

`\begin{aligned}\#\text{ green counters} &= 12 - (3 + 1 + 2) \\ &= 12 - 6 \\ &= 6\end{aligned}`

So, there are 6 green counters.

Next, we can add this to the number of yellow counters to get the number of desired outcomes:

`\begin{aligned}\# \text{ desired outcomes} &= 6 + 2\\ &= 8\end{aligned}`

We are given that there are 12 counters total in the bag, so this is the number of total outcomes:

`\# \text{ total outcomes} = 12`

Finally, we can calculate the probability of pulling a green or yellow counter from a bag with 12 counters using the above definition of probability.

`P = \frac{\#\text{ desired outcomes}}{\#\text{ total outcomes}}`

`P(\text{green or yellow}) &= (8)/(12) \\ \\ \text{ } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \, \boxed{&= (2)/(3)}`

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Note: All of your steps were correct except for the addition, which is circled in the attached image.