Question

In the word MATHEMATICS, find the probability of getting : (a) vowel, (b) consonant and (c) A .

Answer 1

Given:

A word MATHEMATICS

To find:

Probability of

1. Getting a vowel.
2. Getting a consonant.
3. Getting an A.

Solution:

• Probability for any possible event is given by

      $P(E)=\frac{No -of -possible-outcomes}{Total-number-of-outcomes}$

In the given word MATHEMATICS, there are 11 words and the probability of getting each of them is equal.

Hence, the total number of outcomes $n(E)$ are 11.

Step 1

In the word MATHEMATICS , number of vowels are

Vowels = { $A,E,A,I$ }

$n(V)=4$

Therefore,

$P$( Getting a vowel ) = $\frac{n(V)}{n(E)}$

Substituting the given values, we get

$P$(Getting a vowel) = $\frac{4}{11}$

Step 2

Now,

Consonants in the word MATHEMATICS are { $M,T,H,M,T,C,S$ }

$n(C)=7$

Therefore,

$P$(Getting a consonant) $=\frac{n(C)}{n(E)}$

$P$(Getting a consonant) = $\frac{7}{11}$

Step 3

Number of As in the word MATHEMATICS is 2

$n(A)=2$

Hence,

$P$(Getting an A) = $\frac{n(A)}{n(E)}$

$P$(Getting an A) = $\frac{2}{11}$  

Final answer:

Hence,

1. Probability of getting a vowel is $\frac{4}{11}$.
2. Probability of getting a consonant is $\frac{7}{11}$.
3. Probability of getting an A is $\frac{2}{11}$.

Answer 2

Concept

The probability is the likeliness of happening of an event among all the events.

Given

Word " MATHEMATICS"

To find

probability of getting vowel and consonant.

Explanation

In the word MATHEMATICS the number of vowels are 4 and the number of consonants are 7.

The probability of getting vowel(a ,a ,e , i ) is =4/11

The probability of getting consonant(m, t , h , m , t , s ) =7/11

The probability of getting A = 2/11

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