Question

during an experiment, a spinner landed on green 9 times, which resulted in an experimental probability of 1/6. 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 1/5, not 1/6. mary multiplied the 9 occurrences by 6 instead of 5. mary mistakenly thought that 1/6 was the simplest form of 6/45. if there were 9 occurrences, the simplified experimental probability would be 1/7, not 1/6.

Explanation:

Step1: Recall probability formula

The formula for experimental probability $P$ is $P=\frac{\text{number of favorable outcomes}}{\text{total number of trials}}$. Here, the number of favorable outcomes (land - ing on green) is 9, and let the total number of trials be $n$. The experimental probability is given as $\frac{1}{6}$, so $\frac{9}{n}=\frac{1}{6}$. Cross - multiplying gives $n = 54$.

Step2: Analyze Mary's claim

If there were 9 occurrences and 45 trials, the experimental probability would be $\frac{9}{45}=\frac{1}{5}$, not $\frac{1}{6}$.

Answer:

If there were 9 occurrences and 45 trials, the simplified experimental probability would be $\frac{1}{5}$, not $\frac{1}{6}$.