Question

the table shows the results of the experiment to determine the 9 - day weather forecast. how does the experimental probability compare to the theoretical probability? the theoretical probability for rain is $\frac{1}{5}$. the experimental probability for rain is < the actual weather is < the theoretical probability.

Explanation:

Step1: Calculate the experimental probability for rain

Experimental probability formula is \(P=\frac{\text{Frequency of event}}{\text{Total number of trials}}\).
Total number of trials (days) \(=30 + 33+15 + 12=90\).
Frequency of rain \( = 15\).
So, \(P(\text{rain})=\frac{15}{90}=\frac{1}{6}\approx0.17\).

Step2: Calculate the theoretical probability for rain

Theoretical probability for rain is given as \(\frac{1}{5}=0.2\).

Step3: Compare the two probabilities

\(\frac{1}{6}\approx0.17\) and \(\frac{1}{5} = 0.2\).
Since \(0.17<0.2\), the experimental probability for rain is less than the theoretical probability.

Answer:

The experimental probability for rain (\(\frac{1}{6}\)) is less than the theoretical probability (\(\frac{1}{5}\)).