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Given the conditional relative frequency table below, which compares the outside temperature each day to whether it rained that day:

[tex]\[
\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & Rain & No Rain & Total \\
\hline
\begin{tabular}{c}
$80^{\circ} F$ or \\
Greater
\end{tabular} & 0.35 & 0.65 & 1.0 \\
\hline
\begin{tabular}{c}
Less than \\
$80^{\circ} F$
\end{tabular} & 0.3 & 0.7 & 1.0 \\
\hline
Total & $\approx 0.33$ & $\approx 0.67$ & 1.0 \\
\hline
\end{tabular}
\][/tex]

Given that it was less than [tex]$80^{\circ}$[/tex] on a given day, what is the probability that it also rained that day?

A. 0.3
B. 0.35
C. 0.65
D. 0.7

Sagot :

GinnyAnswer
To determine the probability that it rained on a day when the temperature was less than 80°F, we refer to the conditional relative frequency table for the specific values provided.

Here's a detailed, step-by-step solution:

1. Identify the condition:
We are given that the temperature is less than 80°F.

2. Locate the corresponding row:
From the table, find the row where the temperature is "Less than 80°F".

3. Read the probabilities in that row:
In the row labeled "Less than 80°F," we see two probabilities:
- The probability of rain: [tex]\(0.3\)[/tex]
- The probability of no rain: [tex]\(0.7\)[/tex]

4. Determine the required probability:
We need the probability that it rained given the temperature is less than 80°F. According to the table:
- Probability (Rain | Temperature < 80°F) = [tex]\(0.3\)[/tex]

Thus, the probability that it rained on a day when the temperature was less than 80°F is [tex]\(0.3\)[/tex]. The correct answer is:

[tex]\[ \boxed{0.3} \][/tex]
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