Question

finding probabilities
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: Count total outcomes

The letters are A, B, C, D, E, F, G, H. So total outcomes \( n = 8 \). So "The number of possible outcomes is 8" is true.

Step2: Identify vowels and consonants

Vowels in these letters: A, E (2 vowels). Consonants: B, C, D, F, G, H (6 consonants).

Step3: Probability of E

Number of E is 1. Probability \( P(E)=\frac{1}{8}
eq\frac{1}{4} \). So "The probability of drawing the tile with E written on it is \( \frac{1}{4} \)" is false.

Step4: Probability of vowel

\( P(\text{vowel})=\frac{2}{8}=\frac{1}{4} \). So " \( P(\text{vowel})=\frac{1}{4} \)" is true.

Step5: \( P(\text{vowel}) + P(\text{consonant}) \)

\( P(\text{vowel})=\frac{2}{8} \), \( P(\text{consonant})=\frac{6}{8} \). Sum: \( \frac{2 + 6}{8}=\frac{8}{8}=1 \). So " \( P(\text{vowel}) + P(\text{consonant})
eq1 \)" is false.

Step6: Simple event

A simple event is one outcome. Choosing one letter at random is one outcome, so it's a simple event. So "Choosing one letter at random is a simple event" 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})

eq1 \): False

• Choosing one letter at random is a simple event: True

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