Question $1.$ Mergers and Acquisition Analysis $[12]$

A healthcare company "NORTHEN CARE" is considering expanding its operations by acquiring one of two firms: Firm A$,$ a pharmaceutical research company, or Firm B$,$ a medical device manufacturer. The company wants to ensure that the acquisition will generate a positive return. Analysts have estimated that there is a $\backslash (60\backslash \%\backslash )$ chance that the company will acquire Firm A$,$ and if they do$,$ there is an $\backslash (72\backslash \%\backslash )$ chance that the acquisition will succeed $($i$.$e$.,$ generate positive returns$).$ According to the market research there is $\backslash (64\backslash \%\backslash )$ that the acquisition will succeed if the company acquire Firm B$.$

$1.$ Using the given information about the acquisitions possibilities:

a$.$ Find the probability that the company's acquisition will generate a positive return. $[2]$

b$.$ If the acquisition was successful, what is the probability that the company acquired Firm A$?\backslash ([2]\backslash )$

$2.$ Analysts published their estimates about the new firm value if the acquisitions are successful:

a$.$ Use the probability distributions on the tables above calculate the expected value and the standard deviation of the Firm A outcomes. $[3]$

b$.$ Use the probability distributions on the tables above calculate the expected value and the standard deviation of the Firm B outcomes. $[3]$

c$.$ Calculate measure of coefficient of variation for Firm A and B$.$ Determine which Firm caries greater risk and explain why?$[2]$