A letter is taken out at random from ‘ASSISTANT’ and another is taken out from “STATISTICS”. The probability that they are the same letters is:Options3/9619/9019/136None

To solve this problem, we need to calculate the total number of letters in each word and the number of each specific letter in each word.

1. The word 'ASSISTANT' has 9 letters in total. The distribution of letters is as follows: A-2, S-2, I-1, T-2, N-1.
2. The word 'STATISTICS' has 10 letters in total. The distribution of letters is as follows: S-3, T-3, A-1, I-2, C-1.

The probability of drawing the same letter from both words is the sum of the probabilities of drawing each specific letter from both words.

1. The probability of drawing an 'A' from both words is (2/9)*(1/10) = 2/90 = 1/45.
2. The probability of drawing an 'S' from both words is (2/9)*(3/10) = 6/90 = 1/15.
3. The probability of drawing an 'I' from both words is (1/9)*(2/10) = 2/90 = 1/45.
4. The probability of drawing a 'T' from both words is (2/9)*(3/10) = 6/90 = 1/15.
5. The probability of drawing an 'N' from both words is (1/9)*(0/10) = 0, because there is no 'N' in 'STATISTICS'.
6. The probability of drawing a 'C' from both words is (0/9)*(1/10) = 0, because there is no 'C' in 'ASSISTANT'.

Adding these probabilities together gives us the total probability of drawing the same letter from both words:

1/45 + 1/15 + 1/45 + 1/15 = 4/45 = 8/90 = 2/22.5

So, the correct answer is None of the given options.