Question

1. sam tossed a coin 10 times and heads turned up nine times.

a) express the experimental probability of turning up heads as a percent.
b) is the experimental probability what you expected? explain.

Explanation:

Step1: Calculate the experimental probability

The formula for experimental probability \(P = \frac{\text{Number of successful outcomes}}{\text{Total number of trials}}\). Here, the number of successful outcomes (heads) is \(n = 9\), and the total number of trials is \(N=10\). So, \(P=\frac{9}{10}\).

Step2: Convert to percentage

To convert a fraction to a percentage, use the formula \(P(\text{percentage})=\frac{9}{10}\times100\%\).

$$ \frac{9}{10}\times100\%=(9\times10)\% = 90\% $$

Step3: Analyze expected probability

The theoretical probability of getting heads in a fair - coin toss is \(P_{theoretical}=\frac{1}{2}=50\%\). The experimental probability is \(90\%\), which is higher than the theoretical probability. This is because when the number of trials (\(n = 10\)) is small, there can be significant deviations from the theoretical probability. As the number of trials increases, the experimental probability is expected to get closer to the theoretical probability.

Answer:

a) \(90\%\)
b) No. The theoretical probability of getting heads in a fair - coin toss is \(50\%\). Since the number of trials (\(n = 10\)) is small, there can be significant deviations from the theoretical probability. As the number of trials increases, the experimental probability is expected to get closer to the theoretical probability.