An investment bank has been asked to underwrite an issue of 10 million shares by a company.

The bank is trying to decide between a best-efforts deal where it charges a fee of $0.2 for each share sold and a firm-commitment deal where it buys the shares for $10 per share.

For the latter deal, the bank considers that the selling price per share is either $10.8 or $9.8.

What are the break-even probabilities of the two selling prices so that the bank is indifferent to the two deals (Assume that all 10 million shares are sold out)?