Question

tiles with the letters a, b, c, d, e, f, g, and h written on them are placed in a bag. malik draws out one letter at random. which statements about the situation are true? check all that apply. the number of possible outcomes is 8. the probability of drawing the tile with e written on it is $\frac{1}{4}$. $p(vowel)=\frac{1}{4}$. $p(vowel)+p(consonant)
eq1$. choosing one letter at random is a simple event.

Explanation:

Step1: Count total tiles

There are 8 tiles (A, B, C, D, E, F, G, H), so number of possible outcomes is 8. This statement is true.

Step2: Calculate probability of drawing 'E'

There is 1 tile with 'E' out of 8 tiles. So $P(E)=\frac{1}{8}$, not $\frac{1}{4}$. This statement is false.

Step3: Count vowels

Vowels among these are A and E, 2 vowels out of 8 tiles. So $P(\text{vowel})=\frac{2}{8}=\frac{1}{4}$. This statement is true.

Step4: Check vowel - consonant probability sum

Since all letters are either vowels or consonants, $P(\text{vowel})+P(\text{consonant}) = 1$. Given statement $P(\text{vowel})+P(\text{consonant})
eq1$ is false.

Step5: Define simple event

Choosing one letter at random is a single - stage experiment, so it is a simple event. This statement is true.

Answer:

The number of possible outcomes is 8.
$P(\text{vowel})=\frac{1}{4}$
Choosing one letter at random is a simple event.