Quick Share Ltd$.($QSL$),$ a Sydney$-$based IT firm that specialises in providing video sharing services, has a market value of $$150$ million. A rumor starts to circulate in the market that Monster Ltd$,$ a gigantic II firm, is contemplating acquiring QSL$.$ As a result, the market value of QSL has risen sharply to $$185$ million in less than one week. The consensus of market analysts opinion is that QSL has a strategic value of $$200$ million to Monster because QSL$\text{'}$s business fits well with Monster's expansion plan.

$(1)$ Based on the given information, what is the probability of acquisition?

$(2)$ What is the value of synergy if the acquisition goes ahead?

$(3)$ Jack Ma$,$ the chief financial officer at Monster, makes the following recommendation to Monster's board of directors in regard to a potential acquisition offer: $"$QSL has a market value of $$185$ million; therefore it would be reasonable for us to offer $$185$ million plus the synergy value to acquire QSL$"$

Does this recommendation make sense? Please explain.