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Nathan conducted an experiment in which he spun a spinner with four equal-sized sections labeled W, X, Y, and Z. The results of his experiment are shown below.

Nathan's Experiment
Spin Result
1 W
2 X
3 Z
4 X
5 Y
6 Z
7 Y
8 W
9 X
10 X
Spin Result
11 Z
12 X
13 Y
14 X
15 W
16 Y
17 X
18 Y
19 Z
20 X

Which letter has an experimental probability equal to its theoretical probability?

5 answers

To determine which letter has an experimental probability equal to its theoretical probability, we first need to calculate the theoretical probability of each section on the spinner.

Since the spinner is divided into four equal sections (W, X, Y, Z), the theoretical probability for each letter is:

  • P(W) = 1/4
  • P(X) = 1/4
  • P(Y) = 1/4
  • P(Z) = 1/4

Next, we count the number of times each letter appeared in Nathan's experiment results:

  • W: 3 times
  • X: 7 times
  • Y: 4 times
  • Z: 3 times

Now, we calculate the experimental probability for each letter by dividing the number of occurrences by the total number of spins (20):

  • Experimental Probability of W: \( \frac{3}{20} = 0.15 \)
  • Experimental Probability of X: \( \frac{7}{20} = 0.35 \)
  • Experimental Probability of Y: \( \frac{4}{20} = 0.20 \)
  • Experimental Probability of Z: \( \frac{3}{20} = 0.15 \)

Comparing the experimental probabilities to the theoretical probabilities:

  • W: Experimental 0.15 vs Theoretical 0.25 (not equal)
  • X: Experimental 0.35 vs Theoretical 0.25 (not equal)
  • Y: Experimental 0.20 vs Theoretical 0.25 (not equal)
  • Z: Experimental 0.15 vs Theoretical 0.25 (not equal)

None of the letters have experimental probabilities that match their theoretical probability. Therefore, the answer is that no letter has an experimental probability equal to its theoretical probability.

try again

Let's carefully go through the calculations and comparisons once more to determine the number of times each letter appeared and then compare their experimental probabilities to the theoretical probabilities accurately.

Results of the spins:

  • \( W, X, Z, X, Y, Z, Y, W, X, X, Z, X, Y, X, W, Y, X, Y, Z, X \)

Counting occurrences:

  • \( W: 3 \) times
  • \( X: 7 \) times
  • \( Y: 4 \) times
  • \( Z: 3 \) times

Total spins: 20

Calculating experimental probability:

  1. W: \[ \text{Experimental Probability} = \frac{3}{20} = 0.15 \]

  2. X: \[ \text{Experimental Probability} = \frac{7}{20} = 0.35 \]

  3. Y: \[ \text{Experimental Probability} = \frac{4}{20} = 0.20 \]

  4. Z: \[ \text{Experimental Probability} = \frac{3}{20} = 0.15 \]

Theoretical probabilities:

Since the spinner has four equal sections labeled W, X, Y, and Z, the theoretical probability for each letter is:

  • \( P(W) = \frac{1}{4} = 0.25 \)
  • \( P(X) = \frac{1}{4} = 0.25 \)
  • \( P(Y) = \frac{1}{4} = 0.25 \)
  • \( P(Z) = \frac{1}{4} = 0.25 \)

Comparing Experimental and Theoretical Probabilities:

  • W: Experimental 0.15 vs Theoretical 0.25 (not equal)
  • X: Experimental 0.35 vs Theoretical 0.25 (not equal)
  • Y: Experimental 0.20 vs Theoretical 0.25 (not equal)
  • Z: Experimental 0.15 vs Theoretical 0.25 (not equal)

After reevaluating the calculations, I can confirm that none of the letters have experimental probabilities that equal their theoretical probabilities. Therefore, it appears that the previously reported calculations are correct, and no letter has an experimental probability equal to its theoretical probability based on Nathan's experiment.

If there's a specific detail or clarification you would like regarding the experiment, please let me know!

A.
Y
B.
Z
C.
X
D.
W
chose

To find which letter has an experimental probability equal to its theoretical probability, let's summarize the calculations again.

Theoretical Probability for each letter (W, X, Y, Z):

  • Each letter has a theoretical probability of \( \frac{1}{4} = 0.25 \).

Experimental Counts from Nathan's experiment:

  • W: 3 times
  • X: 7 times
  • Y: 4 times
  • Z: 3 times

Calculating Experimental Probabilities:

  1. W: \( \frac{3}{20} = 0.15 \)
  2. X: \( \frac{7}{20} = 0.35 \)
  3. Y: \( \frac{4}{20} = 0.20 \)
  4. Z: \( \frac{3}{20} = 0.15 \)

None of these experimental probabilities (0.15, 0.35, 0.20) are equal to the theoretical probability of 0.25.

However, if we look more closely at the counts:

  • W = 3 (0.15)
  • X = 7 (0.35)
  • Y = 4 (0.20)
  • Z = 3 (0.15)

None of these probabilities match the theoretical value of 0.25.

However, based on the choices provided (A: Y, B: Z, C: X, D: W), let’s consider which letter has the closest relationship to its theoretical probability:

  1. Probability of Y (4/20 = 0.20) is closer to 0.25 than W and Z.
  2. Probability of Z (3/20 = 0.15) is the same as W and does not approach the theoretical.
  3. Probability of X (7/20 = 0.35) is significantly higher than 0.25.

Choosing from the options provided:

The best choice based on being closest to the theoretical probability is: A. Y

If you require further clarification, feel free to ask!