Investment advisors estimated the stock market returns for four market segments: computers, financial, manufacturing, and pharmaceuticals. Annual return projections vary depending on whether the general economic conditions are improving, stable, or declining. The anticipated annual return percentages for each market segment under each economic condition are as follows.

$\backslash$table$[[,$Economic Condition$],[$Market Segment,Improving,Stable,Declining$],[$Computers$,9,2,-4],[$Financial$,8,4,-3],[$Manufacturing$,6,5,-2],[$Pharmaceuticals$,6,4,-1]]$

$($a$)$ Assume that an individual investor wants to select one market segment for a new investment. A forecast shows improving to declining economic conditions with the following probabilities: improving $(0\mathrm{.}2),$ stable $(0\mathrm{.}5),$ and declining $(0\mathrm{.}3).$ What is the preferred market segment for the investor?

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What is the expected return percentage of the preferred market segment?

$\%$

$($b$)$ At a later date, a revised forecast shows a potential for an improvement in economic conditions. New probabilities are as follows: improving $(0\mathrm{.}4),$ stable $(0\mathrm{.}4),$ and declining $(0\mathrm{.}2).$ What is the preferred market segment for the investor based on these new probabilities?

$$

What is the expected return percentage of the preferred market segment?

$$

$\%$