Final answer:
The expected number of complete sets remaining is 1.2, thus the correct option is A.
Step-by-step explanation:
In order to calculate the expected number of complete sets remaining, we must first determine the probability of each set being removed. Since there are a total of 12 blocks and 5 blocks are being removed at random, the probability of each set being removed is 5/12. Therefore, the probability of a set remaining is 1 - 5/12 = 7/12.
Now, we can use the formula for expected value to calculate the expected number of complete sets remaining. The formula is E[X] = ∑ xP(x), where x is the number of complete sets and P(x) is the probability of x occurring.
So, in this case, we have x = 1 complete set remaining and P(x) = 7/12. Plugging these values into the formula, we get E[X] = (1)(7/12) = 7/12 ≈ 1.2.
Explanation part: The question asks us to find the expected number of complete sets remaining after 5 blocks are removed at random from 6 distinct sets of 2 blocks each. This can be calculated by first determining the probability of each set being removed and then using the formula for expected value.
In order to find the probability of each set being removed, we must first find the total number of blocks. Since there are 6 sets with 2 blocks each, the total number of blocks is 6 x 2 = 12. Now, since 5 blocks are being removed at random, the probability of each set being removed is 5/12. This means that there is a 5/12 chance that each set will be removed.
Next, we need to find the probability of a set remaining. This can be done by subtracting the probability of a set being removed (5/12) from 1. So, the probability of a set remaining is 1 - 5/12 = 7/12.
Now, we can use the formula for expected value to calculate the expected number of complete sets remaining. The formula is E[X] = ∑ xP(x), where x is the number of complete sets and P(x) is the probability of x occurring.
In this case, we have x = 1 complete set remaining and P(x) = 7/12. Plugging these values into the formula, we get E[X] = (1)(7/12) = 7/12 ≈ 1.2. This means that on average, we can expect 1.2 complete sets to remain after 5 blocks are removed at random from 6 distinct sets of 2 blocks each, thus the correct option is A.