Probability of drawing no vowel from the word "HOME"

To find the probability of not drawing a vowel from the word "HOME" when two letters are drawn at random, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Favorable Outcomes:
The word "HOME" consists of four letters: H, O, M, and E. Among these letters, there are two vowels (O and E) and two consonants (H and M). Therefore, the favorable outcomes are the combinations of two consonants, which are HM and MH.

Total Possible Outcomes:
To determine the total possible outcomes, we need to calculate the number of ways to choose two letters from the word "HOME". This can be done using the concept of combinations.

The formula for combinations is:
nCr = n! / (r!(n-r)!)

where n represents the total number of items and r represents the number of items to be chosen.

In this case, n = 4 (number of letters in "HOME") and r = 2 (number of letters to be drawn). Plugging these values into the formula, we get:
4C2 = 4! / (2!(4-2)!)
= 4! / (2!2!)
= (4 * 3 * 2 * 1) / ((2 * 1) * (2 * 1))
= 24 / 4
= 6

Therefore, there are a total of 6 possible outcomes when two letters are drawn from the word "HOME".

Calculating the Probability:
The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.

In this case, the number of favorable outcomes is 2 (HM and MH) and the total number of possible outcomes is 6. Therefore, the probability of not drawing a vowel from the word "HOME" is:

P(No vowel) = Number of favorable outcomes / Total number of possible outcomes
= 2 / 6
= 1 / 3

So, the probability of not drawing a vowel from the word "HOME" when two letters are drawn at random is 1/3 or approximately 0.33.

Therefore, the probability of not drawing a vowel from the word "HOME" is 1/3 or approximately 0.33.