A letter is taken out randomly of the word "STATISTICS" and another from "ASSISTANT" what is the probability they are the same letter

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. "STATISTICS" has 10 letters and "ASSISTANT" has 9 letters.

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

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

For S: In "STATISTICS", there are 3 S's. So, the probability of drawing an S is 3/10. In "ASSISTANT", there are 3 S's. So, the probability of drawing an S is 3/9. Therefore, the probability of drawing an S from both words is (3/10) * (3/9) = 9/90 = 1/10.

For T: In "STATISTICS", there are 3 T's. So, the probability of drawing a T is 3/10. In "ASSISTANT", there are 2 T's. So, the probability of drawing a T is 2/9. Therefore, the probability of drawing a T from both words is (3/10) * (2/9) = 6/90 = 1/15.

For A: In "STATISTICS", there is 1 A. So, the probability of drawing an A is 1/10. In "ASSISTANT", there are 3 A's. So, the probability of drawing an A is 3/9. Therefore, the probability of drawing an A from both words is (1/10) * (3/9) = 3/90 = 1/30.

For I: In "STATISTICS", there are 2 I's. So, the probability of drawing an I is 2/10. In "ASSISTANT", there is 1 I. So, the probability of drawing an I is 1/9. Therefore, the probability of drawing an I from both words is (2/10) * (1/9) = 2/90 = 1/45.

Step 4: Add up all the probabilities calculated in step 3 to get the total probability of drawing the same letter from both words.

So, the total probability is 1/10 + 1/15 + 1/30 + 1/45 = 15/90 = 1/6.

Therefore, the probability that the two letters drawn are the same is 1/6.