Quick Share Ltd$.($QSL$),$ a Sydney$-$based IT firm that specialises in providing video sharing services, has a market value of $$150$ million. A rumor starts to circulate in the market that Monster Ltd$,$ a gigantic IT firm, is contemplating acquiring QSL$.$ As a result, the market value of QSL has risen sharply to $$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$$s business fits well with Monster$$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.