Answered

IDNStudy.com, ang perpektong platform para sa mabilis at eksaktong mga sagot. Sumali sa aming platform ng tanong at sagot upang makakuha ng eksaktong tugon sa lahat ng iyong mahahalagang tanong.

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 :

Jafif67556idn

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]