Sowed three varieties of sunflower seeds in a ratio of 2: 3: 5. The probability of immunity to a certain disease

Sowed three varieties of sunflower seeds in a ratio of 2: 3: 5. The probability of immunity to a certain disease in the first, second, third grades is 0.7, 0.6, 0.8, respectively. The seeds, tested at random, turned out to be healthy. Find the probability that these are first grade seeds

First, let’s find the probability that the randomly tested seeds will be first grade seeds.
1) 2 / (2 + 3 + 5) = 2/10 = 0.2 – the probability that the tested seeds are of the first grade.
Since the probability that the seeds of the first grade will be immune to the disease is 0.7, to find the chance of simultaneous triggering of the probabilities, we find their product:
2) 0.2 * 0.7 = 0.14
Answer. The chance that randomly tested seeds that are healthy will be Grade I seeds are 0.14.