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Bronwyn used the spinner pictured below and recorded his results. He spun it 10 times and tallied up how many times he landed on each letter.

C - 2 times

L - 3 times

E - 1 time

A - 2 times

N - 2 times

His experimental probability of landing on the letter L is 310
.



Part 1: What is the theoretical probability of landing on the letter L if the spinner is spun 10 times?

(2 points)
Responses

310
3 tenths

110
1 tenth

210
2 tenths

510
5 tenths
Question 2
Part 2: How do Bronwyn's experimental and theoretical probabilities compare?

Fill in the blank with the correct choice to complete the sentence.

(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Bronwyn's experimental probability of spinning the letter L Response area the theoretical probability of spinning the letter L.

1 answer

To find the theoretical probability of landing on the letter L, we first need to determine the total number of possible outcomes and how many of those outcomes correspond to the letter L.

From the provided information:

  • C = 2 times
  • L = 3 times
  • E = 1 time
  • A = 2 times
  • N = 2 times

The total results after 10 spins is: 2 (C) + 3 (L) + 1 (E) + 2 (A) + 2 (N) = 10.

Now, the theoretical probability of landing on L can be calculated like this: since L was one of the results possible when the spinner was spun, if we assume each letter has an equal chance, the total number of possible outcomes based on the number of letters on the spinner is as follows.

Assuming there are 5 letters on the spinner (C, L, E, A, N), the theoretical probability of L would be:

  • There is 1 L out of 5 possible outcomes.

So, the theoretical probability of landing on the letter L is: \[ P(L) = \frac{1}{5} = 0.2 = \frac{2}{10} = \text{2 tenths}. \]

Answer for Part 1: 210
(2 tenths)

Part 2:

Now, let's compare Bronwyn's experimental probability of landing on L versus the theoretical probability.

From the tally:

  • L was landed on 3 times out of 10 total spins, so the experimental probability is: \[ P(L) = \frac{3}{10} = 0.3. \]

Now, let's fill in the blank for Part 2:

Bronwyn's experimental probability of spinning the letter L is greater than the theoretical probability of spinning the letter L.

Responses for Part 2:
Bronwyn's experimental probability of spinning the letter L is greater than the theoretical probability of spinning the letter L.