Question

A Letter of the English alphabet is chosen at random. Calculate the probability that the letter so chosen
i) is a vowel ii) precedes m and is a vowel iii) follows m and is a vowel.

Answer 1

Answer:

i) 5/26    ii) 3/26   iii) 2/26 = 1/13

Step-by-step explanation:

i) Let the probability of getting a vowel be A

A = { a,e,i,o,u} ; n(A) = 5

n(S) = 26

P(A) = n(A)/ n(S)

       = 5/26

ii) Let the probability of getting a letter preceding m and is a vowel be B

B = { a,e,i } ; n(B) = 3

n(S) = 26

P(B) = n(B)/ n(S)

       = 3/26

iii) let the probability of getting a letter that follows m and is a vowel be C

C = {o,u} ; n(C) = 2

n(S) = 26

P(C) = n(C)/ n(S)

       = 2/26

       = 1/13

Answer 2

Answer:

The answers are: (i) $\frac{5}{26}$ (ii) $\frac{3}{26}$ (iii)

Step-by-step explanation:

As per the data given in the question,

We have,

Total number of english Alphabets = 26

(i) Number of vowels (a,e,i,o,u) = 5

So,

$probability = \frac{Possible\:outcomes}{Total\: outcomes}$

$=\frac{5}{26}$

(ii) vowels preceding m (a,e,i) = 3

$probability = \frac{Possible\:outcomes}{Total\: outcomes}$

$=\frac{3}{26}$

(iii) follows m and is a vowel(o,u) = 2

$probability = \frac{Possible\:outcomes}{Total\: outcomes}$

$\frac{2}{26} = \frac{1}{13}$

Hence,

The answers are: (i) $\frac{5}{26}$ (ii) $\frac{3}{26}$ (iii) $\frac{2}{26} = \frac{1}{13}$

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