Question

the letters in the word mathematics are arranged randomly. write your answers in decimal form. round to the nearest thousandth as needed. what is the probability that the first letter is e? what is the probability that the first letter is m? what is the probability that the first letter is a vowel? what is the probability that the first letter is w?

Explanation:

Step1: Count total letters

The word "MATHEMATICS" has 11 letters.

Step2: Probability of first - letter being E

There is 1 'E' in the word. Probability $P(E)=\frac{1}{11}\approx0.091$.

Step3: Probability of first - letter being M

There are 2 'M's in the word. Probability $P(M)=\frac{2}{11}\approx0.182$.

Step4: Count vowels

The vowels in the word are 'A', 'E', 'A', 'I', so there are 4 vowels. Probability of first - letter being a vowel $P(\text{vowel})=\frac{4}{11}\approx0.364$.

Step5: Probability of first - letter being W

There are 0 'W's in the word. Probability $P(W)=\frac{0}{11}=0$.

Answer:

0.091
0.182
0.364
0