Answer
The gender of a person and the happiness status are not related.
Work Step by Step
To find any association between the gender of a person and their happy status, the conditional probability of gender for provided health status is to be computed. The conditional distribution is the probability distribution of a random variable provided a fixed value for another random variable. So, to obtain the conditional distribution for a variable, the probability of that variable is computed according to the condition that another variable is imposed on it. Conditional distribution probabilities can be calculated using the formula
\[\left( \begin{align}
& \text{Conditional probability of }{{x}_{j}}\text{ variable} \\
& \text{ for given value of }{{y}_{i}}\text{ variable} \\
\end{align} \right)=\frac{\text{Joint frequency of }{{x}_{j}}\text{ and }{{y}_{i}}}{\text{Total frequency of }{{y}_{i}}}\]
Conditional probability of males who are very happy
\[\begin{align}
& =\frac{7609}{11,606} \\
& =0.656
\end{align}\]
Conditional probability of femaleswho are very happy
\[\begin{align}
& =\frac{7942}{12,849} \\
& =0.618 \\
\end{align}\]
Conditional probability of males who are pretty happy
\[\begin{align}
& =\frac{3738}{11,606} \\
& =0.322 \\
\end{align}\]
Conditional probability of females who are pretty happy
\[\begin{align}
& =\frac{4447}{12,849} \\
& =0.346 \\
\end{align}\]
Conditional probability of males who are not too happy
\[\begin{align}
& =\frac{259}{11,606} \\
& =0.022 \\
\end{align}\]
Conditional probability of females who are not too happy
\[\begin{align}
& =\frac{460}{12,849} \\
& =0.036 \\
\end{align}\]
