5. Green Doom, a pesticide used to treat aphid infestations on tomato plants, is applied to 65% of a farmer's crop. It is observed that, of plants treated with the pesticide, 90% will produce a good yield of more than 10 kilograms of tomatoes; this reduces to just 55% for plants not treated with the pesticide. (a) A randomly chosen tomato plant has a yield of 12 kilograms at the end of the growing season. What is the probability that it was treated with Green Doom? Give your answer in the form a/b, where a and b are integers to be found. (b) The manufacturers of Green Doom would like to see at least 85%of tomato plants with a good yield of tomatoes having been treated with the pesticide. What proportion of the farmer's crop must betreated in order to achieve this?