Question

during an experiment, a spinner landed on green 9 times, which resulted in an experimental probability of \\(\frac{1}{5}\\). mary said that there must have been 45 trials in the experiment. why is mary incorrect?\

• if there were 9 occurrences and 45 trials, the simplified experimental probability would be \\(\frac{1}{5}\\), not \\(\frac{1}{6}\\).\
• mary multiplied the 9 occurrences by 6 instead of 5.\
• mary mistakenly thought that \\(\frac{1}{6}\\) was the simplest form of \\(\frac{9}{45}\\).\
• if there were 9 occurrences, the simplified experimental probability would be \\(\frac{1}{7}\\), not \\(\frac{1}{6}\\).

Explanation:

The experimental probability is calculated as the number of successful outcomes (green landings, 9) divided by the total number of trials (let's call it \( n \)). The correct experimental probability was \( \frac{1}{5} \), so \( \frac{9}{n}=\frac{1}{5} \), solving for \( n \) gives \( n = 9\times5=45 \) trials. If Mary thought the simplified form was \( \frac{1}{6} \), she would have incorrectly calculated \( n=9\times6 = 54 \) (or made a mistake in the multiplier for simplifying \( \frac{9}{45} \), since \( \frac{9}{45}=\frac{9\div9}{45\div9}=\frac{1}{5} \), not \( \frac{1}{6} \) as she thought—implying she used 6 as the divisor instead of 5 when simplifying, which is equivalent to multiplying 9 by 6 instead of 5 in the context of finding total trials or simplifying the fraction). So the reason Mary is incorrect is that she multiplied the 9 occurrences by 6 instead of 5.

Answer:

Mary multiplied the 9 occurrences by 6 instead of 5.