Final answer:
To find the probability of getting a type one product, we need to multiply the probability of selecting each factory by the probability of that factory producing a type one product, and then sum those probabilities. The probability of getting a type one product is 0.835 or 83.5%.
Step-by-step explanation:
To find the probability of getting a type one product, we need to multiply the probability of selecting each factory by the probability of that factory producing a type one product, and then sum those probabilities. The probability of selecting each factory is 20%, 30%, and 50%, respectively. The probability of each factory producing a type one product is 90%, 85%, and 80%, respectively.
So, the probability of getting a type one product is:
(20% * 90%) + (30% * 85%) + (50% * 80%) = 0.2 * 0.9 + 0.3 * 0.85 + 0.5 * 0.8 = 0.18 + 0.255 + 0.4 = 0.835.
Therefore, the probability of getting a type one product is 0.835 or 83.5%.