Question

(2 points)
6 yellows
4 greens
2 reds

Using the image above, what is the theoretical probability of picking a yellow counter in simplest form?

30%
50%
70%
100%
Joan picks a random counter out of the bag 10 times, and she got a yellow counter 7 times. What is the experimental probability of picking a yellow?
305
50%
70%
100%

Answer 1

To find the theoretical probability of picking a yellow counter from the bag, we first calculate the total number of counters and then the probability of selecting a yellow counter.

1. **Total counters**:
- Yellow counters: 6
- Green counters: 4
- Red counters: 2

Total = 6 + 4 + 2 = 12 counters.

2. **Theoretical probability of picking a yellow counter**:
\[
P(\text{yellow}) = \frac{\text{Number of yellow counters}}{\text{Total number of counters}} = \frac{6}{12} = \frac{1}{2} = 50\%
\]

So, the theoretical probability of picking a yellow counter is **50%**.

For the second part of your question:

To calculate the experimental probability of picking a yellow counter based on Joan's results:

1. Joan picked a yellow counter 7 times out of 10 total picks.

2. **Experimental probability of picking a yellow counter**:
\[
P(\text{yellow}) = \frac{\text{Number of yellow counters picked}}{\text{Total picks}} = \frac{7}{10} = 70\%
\]

Thus, the experimental probability of picking a yellow counter is **70%**.

To summarize:
- Theoretical probability of yellow: **50%**
- Experimental probability of yellow: **70%**