Chapter 10.3, Problem 13E

(a)

To determine

To find: the probability that patient located in Saratoga was satisfied with the communication of the physicians.

Answer to Problem 13E

The probability that patient located in Saratoga was satisfied with the communication of the physicians.is about $0.789$ .

Explanation of Solution

Given:

		Location
	Glens falls	Saratoga	Albany
Response	Yes	$0.123$	$0.288$	$0.338$
	No	$0.042$	$0.077$	$0.131$

Calculation:

The probability that a randomly selected patient located in Saratoga was satisfied with the communication of the physician is,

  $\begin{array}{l}P\left(yes|saratoga\right)=\frac{P\left(saratogaandyes\right)}{P\left(saratoga\right)}\\ \text{ =}\frac{0.288}{0.288+0.077}\\ \text{ =0}\text{.789}\end{array}$

Thus, the probability that a randomly selected patient located in Saratoga was satisfied with the communication of the physician is about $\boxed{0.789}$ .

Conclusion:

Hence, the probability that patient located in Saratoga was satisfied with the communication of the physicians.is about $0.789$ .

(b)

To determine

To find: the probability that patient located in Glens Falls was not satisfied with the communication of the physicians.

Answer to Problem 13E

The probability that patient located in Glens Falls was not satisfied with the communication of the physicians is $1.168$ .

Explanation of Solution

Calculation:

The probability that a randomly selected patient who was not satisfied with the physician’s communication located in Glens Falls is,

  $\begin{array}{l}P\left(glensfalls|no\right)=\frac{P\left(noandglensfalls\right)}{P\left(no\right)}\\ \text{ =}\frac{0.042}{0.131+0.042+0.077}\\ \text{ =}\boxed{1.168}.\end{array}$

Conclusion:

The probability that patient located in Glens Falls was not satisfied with the communication of the physicians is $1.168$ .

(c)

To determine

To find: whether the satisfaction with the communications of the physician and living in the Saratoga are independent events.

Answer to Problem 13E

Here the two events, communications of the physician and living in the Saratoga are independent events.

Explanation of Solution

Calculation:

The probabilities are,

  $\begin{array}{l}P\left(saratoga\right)=0.288+0.077=0.365\\ P\left(saratoga|yes\right)=0.384\\ AsP\left(saratoga\right)\ne P\left(saratoga|yes\right)\end{array}$

Thus, the two events are indepent.

Conclusion:

Hence the two events, communications of the physician and living in the Saratoga are independent events.