the letters in the word mathematics are arranged randomly. what is the probability that the first letter is…

Explanation:

Step1: Count total letters

The word "MATHEMATICS" has 11 letters.

Step2: Calculate probability of first - letter being E

There is 1 'E' in the word. Probability $P(E)=\frac{\text{Number of 'E's}}{\text{Total number of letters}}=\frac{1}{11}$.

Step3: Calculate probability of first - letter being M

There are 2 'M's in the word. Probability $P(M)=\frac{\text{Number of 'M's}}{\text{Total number of letters}}=\frac{2}{11}$.

Answer:

The probability that the first letter is E is $\frac{1}{11}$. The probability that the first letter is M is $\frac{2}{11}$.