Let's walk through the steps to determine how the experimental probability for rain compares to the theoretical probability.
### Given Data:
- Predicted frequency of rain: 18 days
- Observed frequency of rain: 15 days
- Total days: 90 days
- Theoretical probability for rain: [tex]\( \frac{1}{5} \)[/tex]
### Step 1: Calculate the Experimental Probability for Rain
The experimental probability is calculated using the observed frequency divided by the total number of days.
[tex]\[
\text{Experimental Probability} = \frac{\text{Observed Frequency}}{\text{Total Days}} = \frac{15}{90}
\][/tex]
Simplifying [tex]\(\frac{15}{90}\)[/tex]:
[tex]\[
\text{Experimental Probability} = \frac{1}{6} = 0.16666666666666666
\][/tex]
### Step 2: Compare the Experimental Probability to the Theoretical Probability
- The theoretical probability for rain is [tex]\( \frac{1}{5} = 0.2 \)[/tex].
### Step 3: Determine How the Actual Weather Compares to the Theoretical Probability
- Experimental Probability: [tex]\( 0.1667 \)[/tex] (approx)
- Theoretical Probability: [tex]\( 0.2 \)[/tex]
We need to compare these two probabilities:
- If experimental probability [tex]\( > \)[/tex] theoretical probability
- If experimental probability [tex]\( < \)[/tex] theoretical probability
- If experimental probability [tex]\( = \)[/tex] theoretical probability
Here, [tex]\( 0.1667 \)[/tex] is less than [tex]\( 0.2 \)[/tex].
### Conclusion
The experimental probability for rain is [tex]\( 0.1667 \)[/tex]. This means the actual weather is less than the theoretical probability.
So, we can fill in the blanks as follows:
The theoretical probability for rain is [tex]\( \frac{1}{5} \)[/tex]. The experimental probability for rain is [tex]\( 0.1667 \)[/tex]. The actual weather is [tex]\( \text{less than} \)[/tex] the theoretical probability.
