Given the problem above, we are required to find the probability of getting the letter 'M' when selecting a card at random from a bowl that contains all the letters of the word 'MATHEMATICS' each written on a different card.
Here are the steps we should follow:
1. First, count the number of occurrences of 'M' in the word 'MATHEMATICS'. Going through each letter in the word, we find that the letter 'M' appears twice.
2. Next, to calculate the total sample space (which is essentially the total number of outcomes that are possible), count the total number of letters in the word 'MATHEMATICS'. On doing this, we find that there are a total of 11 letters.
3. Finally, to find the probability of drawing a card with the letter 'M', we need to divide the number of occurrences of 'M' (i.e., 2) by the total number of letters (i.e., 11). When this division is done, we get a probability of approximately 0.1818, which translates to 2/11 as a fraction.
Therefore, the answer is (A) 2/11. This means that if a card is selected randomly from the given bowl, there is a 2 in 11 chance that it will be a card with the letter 'M'.