Question

experimenting with a weather forecast
90-day forecast

weather type	predicted frequency	observed frequency
rain	18	15
clouds	27	33
sunshine	36	30

the table shows the results of the experiment to determine the 90-day weather forecast. how does the experimental probability compare to the theoretical probability?
the theoretical probability for rain is 1/5. the experimental probability for rain is
the actual weather is the theoretical probability.

Explanation:

Step1: Calculate total observed days

$12 + 15 + 33 + 30 = 90$

Step2: Find experimental rain probability

$\frac{\text{Observed rain days}}{\text{Total observed days}} = \frac{15}{90} = \frac{1}{6}$

Step3: Compare probabilities

$\frac{1}{6} \approx 0.167$, $\frac{1}{5} = 0.2$. $\frac{1}{6} < \frac{1}{5}$

Answer:

The experimental probability for rain is $\frac{1}{5}$.
The actual weather is less than the theoretical probability.