If two letters are randomly taken one after the other from the word AUGUST, what is the probability

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01 Aug 2019 Probability

If two letters are randomly taken one after the other from the word AUGUST, what is the probability that none of the letters would be vowels?

OPtion

1) 1/6
2) 2/7
3) 4/5
4) 1/5
5) 2/5
6) 3/11
7) 2/9
8) 3/13
9) 4/11
10) None of these

Solution

Number of vowels in AUGUST = 3
Number of consonants in AUGUST = 3
Total number of alphabets in AUGUST = 6

P(first letter is not vowel) = 3/6

P(second letter is not vowel) = 2/5

So, probability that none of letters would be vowels is = (3/6) × (2/5) = 1/5

Correct Option: 4 Best Solution (7)

Varun   5 years AGO

Vowels V = A U U
Consonants C = G S T
Probability of getting C = 3/6
Probability of getting C again = 2/5
So total = 3/6*2/5 = 6/30 = 1/5 = Option (4)
If it is taken with replacement back of C than it is 3/6*3/6 = 1/4 which is not there in option.
So it is without replacement : )

Like? Yes (3) | No   

Devendra Marghade   5 years AGO

From AUGUST, 6 letter word, ways of choosing 2 letter= 6C2
In AUGUST non-vowel letters are GST, total 3.
Ways of choosing 2 non-vowel letters from 3 = 3C2
Hence, required probability=3C2/6C2=3/15=1/5
Option 4)

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Ashwin Dhina   5 years AGO

3 letters are vowels 3 are not.

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Elizabeth Pothen   5 years AGO

No. of consonents in the word = 3
So probability = (3/6) * (2/5) = 1/5

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G.S.Kantharao   5 years AGO

3c2/6c2=3/15=1/5
My option is 4👈

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Rohini GV   5 years AGO

6C2=15
2 letters=3 combinations
=>3/15
=1/15

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Sukrutha   5 years AGO

6C2=15
No of combinations without vowels is 3
3/15=1/5

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