Question

2) If one letter is chosen from the word “MATHEMATICS” find the probability of:
(a) Getting M
(b) Getting S
(c) Getting a vowel
(d) Getting A.​

Answer 1

Answer :–

a) Probability for getting M = $\dfrac{2}{11}$

b) Probability for getting S = $\dfrac{1}{11}$

c) Probability for getting vowels = $\dfrac{4}{11}$

d) Probability for getting A = $\dfrac{2}{11}$

Given :–

• A word = MATHEMATICS.

To Find :–

Probability of :-

1. Getting M letter in the given word.
2. Getting S letter in the given word.
3. Getting vowels in the given word.
4. Getting A in the given word.

Solution :–

1. Getting M letter.

Probability of getting M letter,

$\sf \red{ \dfrac{Number \: of \: M \: in \: the \: word}{Total \: number \: letters \: in \: the \: word} }$

In the given word, MATHEMATICS.

• Number of M = 2.
• Total number of letters in the given word = 11.

So, the probability of getting M in the given word is,

$\rightarrow \dfrac{2}{11}$

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2. Getting S letter.

Probability of getting S letter,

$\sf \red{\dfrac{Number \: of \: M \: in \: the \: word}{Total \: number \: letters \: in \: the \: word} }$

In the given word, MATHEMATICS.

• Number of S = 1.
• Total number of letters in the given word = 11.

So, the probability of getting S in the given word is,

$\rightarrow \dfrac{1}{11}$

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3. Getting vowels.

Probability of getting vowels,

$\sf \red{ \dfrac{Number \: of \: vowels \: in \: the \: word}{Total \: number \: letters \: in \: the \: word}}$

• Number of vowels (a, e, i, o and u) = 4.
• Total number of letters in the given word = 11.

So, the probability of getting vowels in the given word is,

$\rightarrow \dfrac{4}{11}$

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4. Getting A letter.

Probability of getting A letter,

$\sf \red{\dfrac{Number \: of \: A \: in \: the \: word}{Total \: number \: letters \: in \: the \: word} }$

• Number of A = 2.
• Total number of letters in the given word = 11.

So, the probability of getting A letter in the given word is,

$\rightarrow \dfrac{2}{11}$

Answer 2

$\large \sf \implies \: given \: \\ \\ \bullet \: \sf \: a \: word \:{ \red{ \bold{ MATHEMATICS}}} \\ \\ \sf \large \implies To \: Find \\ \sf \bullet \: \: the \: probability \: of: \\ </p><p>\sf \bullet \:(a) Getting \: M \\ \sf \bullet \:</p><p>(b) Getting \: S \\ \sf \bullet \:</p><p>(c) Getting \: a \: vowel \\ \sf \bullet \:</p><p>(d) Getting \: A. \\ \\ \sf \implies \large Solution : \\ \\ \triangleright \sf \: total \: words \: = 11 \\ \\ \sf \implies { \boxed{ \bold{probability \: = \frac{Number \: of \: given \: observation}{ \: total \: Number \: of \: observation}}}} \\ \\ \triangleright \sf \: a) \: probability \: of \: getting \: M \: = \frac{2}{11} \\ \\ \triangleright \sf \:b) \: probability \: of \: getting \: S \: = \frac{1}{11} \\ \\ \triangleright \sf \: c) \: probability \: of \: getting \:vowel \: = \frac{4}{11} \\ \\ \triangleright \: \sf d) probability \: of \: getting \:A \: = \frac{2}{11}$