Question

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. responses greater then or less then

Answer 1

To answer these questions, we will first determine the theoretical probability of landing on the letter L, and then compare it with the experimental probability.

Part 1: Theoretical Probability of L From the results given, Bronwyn spun the spinner a total of 10 times, and landed on L a total of 3 times. The theoretical probability is based on the expected outcomes.

If we assume that all letters on the spinner are equally likely (which we cannot verify with the provided information, but it's a common assumption when presented with a spinner with unknown sections), the theoretical probability of landing on L would be based on the ratio of how many times L appears compared to the total number of possible outcomes (which we'll assume to be the same distribution).

From the tally:

• Total spins = 10
• Spins on L = 3

Thus, the theoretical probability of landing on L is: \[ \text{Probability of L} = \frac{\text{Number of times landed on L}}{\text{Total number of spins}} = \frac{3}{10} = 3 \text{ tenths} \]

So, the correct response is 3 tenths.

Part 2: Comparison of Experimental and Theoretical Probabilities

• Bronwyn's experimental probability of landing on L is given as \( \frac{3}{10} \).
• Our calculation for the theoretical probability is also \( \frac{3}{10} \).

Thus we can complete the sentence: "Bronwyn's experimental probability of spinning the letter L is equal to the theoretical probability of spinning the letter L."

Since the options provided for the blank are "greater than" or "less than", the appropriate choice would be neither, but since both probabilities are equal, we can assert that they compare favorably. If forced to choose from given responses of greater or less, it would mean they present a mismatch in wording options; thus the respondent should clarify this inconsistency.

In brief:

• Experimental probability is equal to theoretical probability, so they are comparable positively.