a. "P(Gas\\; shortage\\;\\; OR\\;\\; Mechanical\\; problem)=\\frac{25+20-15}{100}=0.3."
b. "P(Mechanical\\;problem|Gas\\;shortage)=\\frac{15}{25}=0.6."
c. "P(Gas\\;shortage\\;\\;AND\\;\\;Mechanical \\;problem)=\\frac{15}{100}=0.15."
"P(Gas\\;shortage)*P(Mechanical\\;problem)=\\frac{25}{100}*\\frac{20}{100}=0.05."
Since "0.15\\ne0.05," gas shortage and mechanical problem are not independent.
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