Question

a letter in the word electric is chosen at random. complete each sentence. there are □ possible outcomes. the theoretical probability that a vowel will not be chosen is the ratio □. the theoretical probability that the letter n will be chosen is □.

Explanation:

Part 1: Number of possible outcomes

Step1: Count letters in "ELECTRIC"

The word "ELECTRIC" has letters: E, L, E, C, T, R, I, C. Let's count them: E (1), L (2), E (3), C (4), T (5), R (6), I (7), C (8). Wait, wait, let's list all unique? No, total letters. Wait, E, L, E, C, T, R, I, C. Wait, that's 8? Wait no: E, L, E, C, T, R, I, C. Wait, E (2), L (1), C (2), T (1), R (1), I (1). Total letters: 2 + 1 + 2 + 1 + 1 + 1 = 8? Wait no, let's write them out: E, L, E, C, T, R, I, C. Wait, that's 8 letters? Wait, E (2), L (1), C (2), T (1), R (1), I (1). So total number of letters (including repeats) is 8? Wait, no: E, L, E, C, T, R, I, C. Let's count: 1.E, 2.L, 3.E, 4.C, 5.T, 6.R, 7.I, 8.C. Yes, 8 letters. Wait, but wait, maybe I made a mistake. Let's check the spelling: E-L-E-C-T-R-I-C. Yes, that's 8 letters. So the number of possible outcomes is the number of letters, which is 8? Wait, no, wait: E, L, E, C, T, R, I, C. Wait, E (2), L (1), C (2), T (1), R (1), I (1). So total letters: 2 + 1 + 2 + 1 + 1 + 1 = 8. So possible outcomes: 8. Wait, but wait, maybe I miscounted. Let's write each letter:

1. E
2. L
3. E
4. C
5. T
6. R
7. I
8. C

Yes, 8 letters. So the number of possible outcomes is 8.

Part 2: Probability vowel is NOT chosen

Step1: Identify vowels in "ELECTRIC"

Vowels are A, E, I, O, U. In "ELECTRIC", the vowels are E, E, I. So count of vowels: E (2) + I (1) = 3.

Step2: Count consonants (non - vowels)

Total letters: 8. Consonants = Total - Vowels = 8 - 3 = 5.

Step3: Calculate probability (non - vowel)

Probability = $\frac{\text{Number of consonants}}{\text{Total number of letters}}$ = $\frac{5}{8}$.

Part 3: Probability letter N is chosen

Step1: Check if N is in "ELECTRIC"

The word "ELECTRIC" has letters E, L, E, C, T, R, I, C. There is no N. So number of N's = 0.

Step2: Calculate probability

Probability = $\frac{\text{Number of N's}}{\text{Total number of letters}}$ = $\frac{0}{8}$ = 0.

Answer:

s:

• There are $\boldsymbol{8}$ possible outcomes.
• The theoretical probability that a vowel will NOT be chosen is the ratio $\boldsymbol{\frac{5}{8}}$.
• The theoretical probability that the letter N will be chosen is $\boldsymbol{0}$.