Chapter 5.2, Problem 52E

(a)

To determine

Display the outcomes of the chance process with Venn diagram.

Explanation of Solution

Given:

L: reads the Los Angeles Times

W: reads the Wall Street Journal

Draw two partially overlapping ellipses.

Such that

Left ellipse represents L.

Right ellipse represents W.

We know

5% of the guests read both Wall Street Journal and Los Angeles Times .

Thus,

  $\text{L}\cap \text{W}=5\%$

Write 5% in the area where two ellipses are overlapping.

And

40% of the guests read Los Angeles Times , whereas 5% of the guests read both the newspapers.

That implies

35% of the guests read Los Angeles Times but do not read Wall Street Journal .

Thus,

  $\text{L}\cap {\text{W}}^{\text{c}}=35\%$

Write 35% in the part of ellipse L that does not overlap with ellipse W.

And

25% of the guests read Wall Street Journal , whereas 5% of the guests read both the newspapers.

That implies

20% of the guests read Wall Street Journal but do not read Los Angeles Times .

Thus,

  ${\text{L}}^{\text{c}}\cap \text{W}=20\%$

Write 20% in the part of ellipse W that does not overlap with ellipse L.

We also know

Venn diagram requires 100% representation.

Thus,

  $\begin{array}{l}{\text{L}}^{\text{c}}\cup {\text{W}}^{\text{c}}=100\%-\left(\text{L}\cup \text{W}\right)\\ =100\%-60\%\\ =40\%\end{array}$

That implies

40% of the guests do not read any of the two newspapers.

Then

Write 40% in the area outside both the ellipses.

  

(b)

To determine

Probability for the event ${\text{L}}^{\text{c}}\cap \text{W}$ .

Answer to Problem 52E

Probability for the event,

  $P\left({\text{L}}^{\text{c}}\cap \text{W}\right)=0.20$

Explanation of Solution

Given:

L: reads the Los Angeles Times

W: reads the Wall Street Journal

Calculations:

  ${\text{L}}^{\text{c}}$ : does not read Los Angeles Times

  ${\text{W}}^{\text{c}}$ : does not read Wall Street Journal

Note that

In the Venn diagram,

The part of ellipse W that does not overlap with the corresponding ellipse L comprises of 20%.

That implies

20% of the guests do not read Los Angeles Times and read only Wall Street Journal .

Thus,

The probability for the event,

  $P\left({\text{L}}^{\text{c}}\cap \text{W}\right)=20\%=0.20$