Chapter 4 - Section 4.4 - Assess Your Understanding - Applying the Concepts - Page 243: 11

The person who is healthy is happier.

To find any association between the health of people and their happy status, the conditional probability of the happier status for the 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 people who are not too happy and their health is poor \[\begin{align} & =\frac{696}{1996} \\ & =0.349 \end{align}\] Conditional probability of people who are not too happy and their health is fair \[\begin{align} & =\frac{1386}{6585} \\ & =0.21 \end{align}\] Conditional probability of people who are not too happy and their health is good \[\begin{align} & =\frac{1629}{15,791} \\ & =0.103 \end{align}\] Conditional probability of people who are not too happy and their health is excellent \[\begin{align} & =\frac{732}{11,022} \\ & =0.066 \end{align}\] Conditional probability of people who are pretty happy and their health is poor \[\begin{align} & =\frac{950}{1996} \\ & =0.476 \end{align}\] Conditional probability of people who are pretty happy and their health is fair \[\begin{align} & =\frac{3817}{6585} \\ & =0.58 \end{align}\] Conditional probability of people who are pretty happy and their health is good \[\begin{align} & =\frac{9642}{15,791} \\ & =0.611 \end{align}\] Conditional probability of people who are pretty happy and their health is excellent \[\begin{align} & =\frac{5195}{11,022} \\ & =0.471 \end{align}\] Conditional probability of people who are very happy and their health is poor \[\begin{align} & =\frac{350}{1996} \\ & =0.175 \end{align}\] Conditional probability of people who are very happy and their health is fair \[\begin{align} & =\frac{1382}{6585} \\ & =0.21 \end{align}\] Conditional probability of people who are very happy and their health is good \[\begin{align} & =\frac{4520}{15,791} \\ & =0.286 \end{align}\] Conditional probability of people who are very happy and their health is excellent \[\begin{align} & =\frac{5095}{11,022} \\ & =0.462 \end{align}\]