Question

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 dropdown. the actual weather is dropdown the theoretical probability. options for the second dropdown: exactly the same as, approximately the same as, the opposite of. weather type | predicted frequency | observed frequency
wind | 9 | 12
rain | 18 | 15
clouds | 27 | 33
sunshine | 36 | 30

Explanation:

Step1: Calculate total observed frequency

$12 + 15+33 + 30=90$

Step2: Calculate experimental probability of rain

The experimental probability of rain is $\frac{\text{Observed frequency of rain}}{\text{Total observed frequency}}=\frac{15}{90}=\frac{1}{6}$

Step3: Compare experimental and theoretical probabilities

The theoretical probability of rain is $\frac{1}{5}=\frac{6}{30}$ and the experimental probability is $\frac{1}{6}=\frac{5}{30}$. Since $\frac{1}{5}\approx\frac{1}{6}$, the actual weather is approximately the same as the theoretical probability.

Answer:

The experimental probability for rain is $\frac{1}{6}$. The actual weather is approximately the same as the theoretical probability.