1 (Independence and Conditional Probabilities) The quality of a manufactured copper wire is being assessed for its tensile strength and conductivity. Sometimes, when the copper wires are produced, they have defects that prevent them from being shipped. To assess this, first, the tensile strength is measured. There is a 90% chance that the manufactured copper wire has sufficient tensile strength to be shipped. Second, the conductivity is measured. If the copper wire has insufficient tensile strength, there is an 85% chance that the copper wire has sufficient conductivity to be shipped. If the copper wire has sufficient tensile strength, there is a 70% chance that the copper wire has sufficient conductivity to be shipped. a) Calculate the probability that a manufactured copper wire has sufficient conductivity to be shipped (irrespective of whether its tensile strength is sufficient or not). (3 marks) b) Are the two events - of the copper wire having sufficient tensile strength, and the copper wire having sufficient conductivity - independent events? Explain your answer. (1 mark)