Probability of Drawing Tiles Analysis
To answer the questions provided in the image:
1. Will all the possible outcomes appear to be equally likely based on the observed frequencies?
To determine if all outcomes are equally likely, we can compare the frequencies of each letter. The frequencies shown in the table are:
- A: 6
- E: 12
- O: 8
- W: 14
The frequencies are not the same for each letter, so the possible outcomes do not appear to be equally likely based on the observed frequencies.
2. What is the experimental probability for drawing a W tile?
To find the experimental probability of drawing a W tile, we use the frequency of the W outcome divided by the total number of outcomes. The total number of outcomes can be found by adding the frequencies of all the letters together:
Total outcomes = 6 (A) + 12 (E) + 8 (O) + 14 (W) = 40
Now, we calculate the experimental probability for W:
Experimental probability for W = Frequency of W / Total outcomes
= 14 / 40
= 0.35
So, the experimental probability of drawing a W tile is 0.35, or 35%.
3. If there were a total of 100 tiles, what is the best estimate of the number of E tiles in the bag?
We look at the frequency distribution to estimate the number of E tiles. From the total of 40 tiles that were drawn (as calculated above), E tiles were drawn 12 times. To find the best estimate for 100 tiles, we can set up a proportion based on the experimental results:
12 (frequency of E) / 40 (total outcomes) = x (estimated number of E tiles) / 100 (total tiles)
Now, solve for x:
(12 / 40) * 100 = x
(0.3) * 100 = x
x = 30
The best estimate for the number of E tiles in a bag of 100 tiles, based on the experimental probability, is 30.
