A company is trying to predict the long$-$run market share of a new men's deodorant. Based on initial marketing studies, they believe that $35\%$ of new purchasers in this market will ultimately try this brand, and

of these, about $60\%$ will purchase it in the future. Preliminary data also suggest that the brand will attract heavier$-$than$-$average buyers, such as those who exercise frequently and participate in sports, and that

they will purchase about $20\%$ more than the average buyer. Complete parts a and $b.$

a$.$ Calculate the long$-$run market share that the company can anticipate under these assumptions.

The long$-$run market share is

$($Type an integer or a decimal rounded to three decimal places as needed.$)$