Final answer:
The probability that at least one-third of the 12 randomly chosen US workers belong to a trade union is approximately 0.706.
Step-by-step explanation:
To find the probability that at least one-third of the 12 randomly chosen US workers belong to a trade union, we need to consider the percentage of US workers who belong to unions. According to the given information, 11.9% of the total labor force belongs to trade unions.
Since we want to find the probability of at least one-third of the workers being union members, we can calculate the probability of the opposite event, which is none of the workers being union members.
The probability of a worker not belonging to a union is 1 - 0.119 = 0.881. Since we are choosing 12 workers independently, the probability of none of them belonging to a union is (0.881)^12.
So, the probability that at least one-third of the 12 workers belong to a trade union is 1 - (0.881)^12 ≈ 0.706.