Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ There are 12 counters in a bag:

- 3 of the counters are red.
- 1 of the counters is blue.
- 2 of the counters are yellow.
- The rest of the counters are green.

Caitlin takes a counter at random from the bag.

(c) Show that the probability that this counter is yellow or green is [tex]\frac{2}{3}[/tex].

To solve the problem, we need to find the probability that Caitlin picks either a yellow or green counter from the bag.

1. Understand the Total and Individual Counters:
- Total counters in the bag = 12
- Red counters = 3
- Blue counters = 1
- Yellow counters = 2

2. Find the Number of Green Counters:
- Total counters = 12
- Add up counters that are not green (red, blue, yellow):
[tex]$3 \text{ (red)} + 1 \text{ (blue)} + 2 \text{ (yellow)} = 6$[/tex]
- Number of green counters = Total counters - Non-green counters
[tex]$ = 12 - 6 = 6$[/tex]

3. Determine Yellow or Green Counters:
- Yellow counters = 2
- Green counters = 6
- Total yellow or green counters = Yellow counters + Green counters
[tex]$ = 2 + 6 = 8$[/tex]

4. Calculate the Probability:
- Probability of picking a yellow or green counter = Number of yellow or green counters / Total counters
[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].