To determine the model that correctly represents the possible outcomes of James’ experiment of picking a letter tile from the box containing the letters S, M, I, L, and E, we need to consider the probabilities of each letter.
Since there are 5 letters (S, M, I, L, E) and assuming each letter has an equal chance of being chosen, each letter would have a probability of:
\[ \text{Probability of each letter} = \frac{1}{5} = 0.20 \]
This is equivalent to 20% for each letter.
Now, let's analyze each of the potential responses:
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First option: Letters M, I, L, and E with probabilities all at 1%. This is incorrect as it only includes four letters and the probabilities do not add up to 100%.
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Second option: Letters S, M, I, L, and E with probabilities S = 0.15, M = 0.20, I = 0.30, L = 0.20, E = 0.15. This is incorrect because the probabilities do not equal 1 (0.15 + 0.20 + 0.30 + 0.20 + 0.15 = 1.00); however, they do not align with equal probabilities for all letters.
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Third option: Letters M, I, L, and E with probabilities all at 20%. This is incorrect as it only includes four letters and omits letter S.
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Fourth option: Letters S, M, I, L, and E with probabilities approximately 0.20 for each. This is correct as it includes all five letters with equal probabilities of 0.20.
From this analysis, the fourth option accurately represents the possible outcomes of picking a letter from the word SMILE, where each of the five letters has an equal probability of being chosen.
Thus, the correct model is the fourth option.