Question

pre-algebra ic sem 2 fall 2025
experimental vs. theoretical probability
90-day forecast
weather
type
sunshine
clouds
rain
wind
predicted
frequency
36
27
18
9
observed
frequency
30
33
15
12
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 $\frac{1}{5}$. the
experimental probability for rain is $\frac{1}{6}$
the actual weather is
$gt$
the theoretical probab...
exactly the same as
approximately the
same as
the opposite of

Explanation:

Step1: Calculate theoretical probability

The theoretical probability for rain is \(\frac{1}{5}\).

Step2: Calculate experimental probability

Experimental probability \(P=\frac{\text{Observed frequency of rain}}{\text{Total days}}\). Total days \(=30 + 33+15 + 12=90\). Observed frequency of rain \( = 15\). So \(P=\frac{15}{90}=\frac{1}{6}\approx0.167\). \(\frac{1}{5}=0.2\).

Answer:

The experimental probability (\(\frac{1}{6}\approx0.167\)) is approximately the same as the theoretical probability (\(\frac{1}{5} = 0.2\)) considering small - sample variations.