Chapter 7, Problem 1EA

Find the probability that a randomly selected patient has recent onset of nervousness and is euthyroid.

To determine

The probability that the randomly selected patient has a recent onset of nervousness and is euthyroid.

Answer to Problem 1EA

Solution: $0.37$

Explanation of Solution

Given:

$\begin{array}{l}P\left(T_1\right)=0.15\\ P\left(T_2\right)=0.65\\ P\left(T_3\right)=0.20\end{array}$

Symptom	Hypothyroid$\left(T_1\right)$	Euthyroid$\left(T_2\right)$	Hyperthyroid$\left(T_3\right)$
Recent onset of nervousness (N)	0.06	0.37	0.92
Recent onset of heat sensitivity(H)	0	0.17	0.74
Recent onset of increased sweating (S)	0.13	0.25	0.68
Recent onset of increased appetite (A)	0.03	0.1	0.61
Recent onset of weight loss (W)	0.13	0.45	0.84

Explanation:

Let us consider the events.

Event N$\to$Patient has an onset of nervousness.

Event H$\to$Patient has an onset of heat sensitivity.

Event S$\to$Patient has an onset of increased sweating

Event A$\to$Patient has an onset of increased appetite.

Event W$\to$Patient has an onset of weight loss.

Event $T_1$$\to$Patient is hypothyroid.

Event $T_2$$\to$Patient is euthyroid.

Event $T_3$$\to$Patient is hyperthyroid.

Now, the probability that the randomly selected patient has an onset of nervousness and is euthyroid is denoted by $P\left(N\cap T_2\right)$.

From the provided table, it can be observed that $P\left(N\cap T_2\right)=0.37$.

So, the probability that the randomly selected patient has an onset of nervousness and is euthyroid is $0.37$.

Conclusion: $P\left(N\cap T_2\right)$ is the intersection of $row1$ and $column2$ of the probabilities provided in the table. Hence, the probability that the randomly selected patient has an onset of nervousness and is euthyroid is $0.37$.