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(\text{vowel}) = \frac{1}{4}\\) \\(p(\text{vowel}) + p(\text{consonant}) \
eq 1\\) choosing one letter at random is a simple event.

Explanation:

Step1: Analyze the number of outcomes

There are 8 tiles (A, B, C, D, E, F, G, H), so the number of possible outcomes when drawing one tile is 8. So the first statement is true.

Step2: Probability of drawing E

There is 1 E and 8 total tiles. The probability of drawing E is $\frac{1}{8}$, not $\frac{1}{4}$. So the second statement is false.

Step3: Probability of drawing a vowel

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

Step4: Sum of probabilities of vowel and consonant

Since every tile is either a vowel or a consonant, $P(\text{vowel}) + P(\text{consonant}) = 1$. So the fourth statement is false.

Step5: Simple event definition

A simple event is an event with a single outcome. Choosing one letter at random has a single outcome (drawing one specific letter), so it is a simple event. So the fifth statement is true.

Answer:

• The number of possible outcomes is 8. (True)
• The probability of drawing the tile with E written on it is $\frac{1}{4}$. (False)
• $P(\text{vowel})=\frac{1}{4}$. (True)
• $P(\text{vowel}) + P(\text{consonant})

eq 1$. (False)

• Choosing one letter at random is a simple event. (True)

So the true statements are: "The number of possible outcomes is 8.", "$P(\text{vowel})=\frac{1}{4}$", "Choosing one letter at random is a simple event."