A survey finds that 12% of cardiac pacemakers implanted in Australian patients a

Question

A survey finds that 12% of cardiac pacemakers implanted in Australian patients are manufactured by “Happy Hearts Ltd”. It is known that the Happy Hearts Ltd pacemaker products have a 95% success rate for lasting 5 years from implantation without need for replacement. By comparison, across all other brands of pacemakers used in Australia the 5-year success rate is 82%. For a randomly chosen patient who received a cardiac pacemaker 5 years ago and has not required a replacement, what is the probability that they received a Happy Hearts Ltd pacemaker?

Explanation / Answer

probabilty of Happy Hearts ltd product =P(HHL)=0.12

probbilty of other company =P(O)=1-0.12=0.88

hence probabilty that product will survive 5 years =P(>5) =0.12*0.95+0.88*0.82=0.8356

probability that they received a Happy Hearts Ltd pacemaker, given survives 5 years =P(HHL|>5)

=P(HHL)*P(>5|HHL)/P(>5)=0.12*0.95/0.8356=0.136429

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