The case fatality rate ($CFR$) of a disease is the ratio of the number of deaths from the disease to the total number of people diagnosed with the disease (“patients”), and is usually expressed as a percentage. It has been reported that the $CFR$ of Pandemic-$20$ among elderly people in Gondwanaland is $20\%$. One way of treating a Pandemic-$20$ patient involves putting the patient on a ventilator. It has been observed that in Gondwanaland, $60\%$ of the elderly Pandemic-$20$ patients who survied the disease had been put on a ventilator, and $10\%$ of the elderly Pandamic-$20$ patients who died from the disease had been put on a ventilator. What is the probability that an elderly Pandamic-$20$ patient in Gondwanaland survives the disease if they were put on a ventilator as part of the treatment?
