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You have nine bags and in each bag you put a letter from the word "NEUMATICO" (5 vowels and 4 consonants. You pick two bags randomly. You open one of the picked bags and you see a vowel. What is the probability that the other bag contains a consonant?

I think the probability is 1/2 since you know that a vowel is in the first bag, then four consonants remains from a total of eight letters, hence 4/8 = 1/2.

Thanks your your help.

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  • $\begingroup$ Seems plausible to me. $\endgroup$ – Peter Nov 21 '15 at 13:51
  • $\begingroup$ Are they put in same order as they appear. $\endgroup$ – Archis Welankar Nov 21 '15 at 14:05
  • $\begingroup$ The order doesn't matter. $\endgroup$ – Carlitos_30 Nov 21 '15 at 15:15
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Since you opened a bag at random, the other bags still have equal distribution, therefore your answer is correct. Be aware though that if someone else opens the bag for you knowing he'll find a vowel the probability changes (it's the famous Monty-Hall "paradox")

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