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:

To solve this problem, we need to calculate the probability of drawing the same letter from both words.

Step 1: Count the number of letters in each word. 'ASSISTANT' has 9 letters and 'STATISTICS' has 10 letters.

Step 2: Identify the common letters in both words. The common letters are: A, S, T, I.

Step 3: Calculate the probability of drawing each common letter from both words.

• For 'A': In 'ASSISTANT', there is 1 'A' out of 9 letters. So, the probability is 1/9. In 'STATISTICS', there is 1 'A' out of 10 letters. So, the probability is 1/10. The combined probability is (1/9) * (1/10) = 1/90.

• For 'S': In 'ASSISTANT', there are 2 'S' out of 9 letters. So, the probability is 2/9. In 'STATISTICS', there are 3 'S' out of 10 letters. So, the probability is 3/10. The combined probability is (2/9) * (3/10) = 6/90 = 1/15.

• For 'T': In 'ASSISTANT', there are 2 'T' out of 9 letters. So, the probability is 2/9. In 'STATISTICS', there are 3 'T' out of 10 letters. So, the probability is 3/10. The combined probability is (2/9) * (3/10) = 6/90 = 1/15.

• For 'I': In 'ASSISTANT', there is 1 'I' out of 9 letters. So, the probability is 1/9. In 'STATISTICS', there is 1 'I' out of 10 letters. So, the probability is 1/10. The combined probability is (1/9) * (1/10) = 1/90.

Step 4: Add up all the combined probabilities. 1/90 + 1/15 + 1/15 + 1/90 = 2/90 + 6/90 + 6/90 + 2/90 = 16/90 = 8/45.

So, the probability that the same letter is drawn from both words is 8/45.