Question

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

Answer 1

To find which letter has an experimental probability equal to its theoretical probability, we first need to determine the theoretical probability for each letter. Since the spinner has four equal-sized 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 need to calculate the experimental probabilities based on Nathan's results. We will count how many times each letter appeared and divide by the total number of spins (20).

**Counting Results:**
- W: 4 times (Spins 1, 8, 15)
- X: 7 times (Spins 2, 4, 9, 10, 12, 14, 17)
- Y: 4 times (Spins 5, 7, 16, 18)
- Z: 5 times (Spins 3, 6, 11, 19)

**Calculating Experimental Probabilities:**
- P(W) = 4/20 = 1/5
- P(X) = 7/20
- P(Y) = 4/20 = 1/5
- P(Z) = 5/20 = 1/4

Now we compare the experimental probabilities to the theoretical probabilities:
- For W: Experimental (1/5) vs Theoretical (1/4) - Not equal
- For X: Experimental (7/20) vs Theoretical (1/4) - Not equal
- For Y: Experimental (1/5) vs Theoretical (1/4) - Not equal
- For Z: Experimental (1/4) vs Theoretical (1/4) - Equal

The letter that has an experimental probability equal to its theoretical probability is **C. Z**.