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Maricar labeled each of 26 small pieces of paper a distinct letter in the English alphabet. She put it in a box. If she will ask her brother, Paulo, to randomly pick a piece of paper from the box, what is the probability that it is:

1. a vowel or a consonant?
2. a consonant or w?
3. a vowel or e
4. a consonant or a?
5. a vowel or k?

Sagot :

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Answer:

Summary of Probabilities

[tex]1. P(\text{vowel or consonant}) = 1 [/tex]

[tex]2. P(\text{consonant or W}) = \frac{21}{26} [/tex]

[tex]3. P(\text{vowel or E}) = \frac{5}{26} [/tex]

[tex]4. P(\text{consonant or A}) = \frac{21}{26} [/tex]

[tex]5. P(\text{vowel or K}) = \frac{5}{26} [/tex]

Thus, the final answers are:

[tex]1. \: \boxed{1} [/tex]

[tex]2. \: \boxed{\frac{21}{26}}[/tex]

[tex]3. \: \boxed{\frac{5}{26}}[/tex]

[tex]4. \: \boxed{\frac{21}{26}} [/tex]

[tex]5. \: \boxed{\frac{5}{26}} [/tex]

Step-by-step explanation:

Total Letters in the English Alphabet

There are 26 letters in the English alphabet.

Vowels and Consonants

The vowels in the English alphabet are: A, E, I, O, U (5 vowels).

The consonants are the remaining letters: B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z (21 consonants).

Probability Formula

The probability P of an event is given by:

[tex]P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}.[/tex]

Now, let's solve each part:

1. Probability of picking a vowel or a consonant

Since every letter is either a vowel or a consonant, the probability is:

[tex]{P(\text{vowel or consonant}) = \frac{26}{26} = 1.}[/tex]

2. Probability of picking a consonant or W

There are 21 consonants and 1 W, but W is already counted as a consonant. Thus, the number of favorable outcomes is 21.

[tex]P(\text{consonant or W}) = \frac{21}{26}.[/tex]

3. Probability of picking a vowel or E

There are 5 vowels, and E is one of them. Thus, the number of favorable outcomes is still 5 (since E is already counted).

[tex]P(\text{vowel or E}) = \frac{5}{26}.[/tex]

4. Probability of picking a consonant or A

There are 21 consonants, and A is a vowel. Thus, the number of favorable outcomes is still 21.

[tex]P(\text{consonant or A}) = \frac{21}{26}.[/tex]

5. Probability of picking a vowel or K

There are 5 vowels, and K is a consonant. Thus, the number of favorable outcomes is still 5.

[tex]P(\text{vowel or K}) = \frac{5}{26}.[/tex]

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