Question 1127738
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In probability, it is useful to understand different methods for finding answers to questions like these.  The answers from the other tutor are correct; and you should understand them and be able to use his methods.<br>
His method is basically to find the number of favorable outcomes for each of the three cases and divide that by the total number of possible outcomes.<br>
I would prefer a different general method for all three parts of the problem: finding the probabilities one letter at a time.<br>
For the first two cases, that makes the problem very easy.<br>
A) begins with a consonant:  3 of the 5 letters are consonants; there are no restrictions on the remaining letters.  The probability is 3/5.<br>
B) ends with a vowel:  in the exact similar way, 2 of the 5 letters are vowels, and there are no other restriction; the probability is 2/5.<br>
C) has the consonants and vowels alternating.  For this case, we have to choose consonants for the 1st, 3rd, and 5th letters, and vowels for the 2nd and 4th.<br>
P(1st a consonant) = 3/5
P(2nd a vowel) = 2/4
P(3rd a consonant) = 2/3
P(4th a vowel) = 1/2
P(5th a consonant) = 1/1<br>
P(alternating consonants and vowels) = (3/5)(2/4)(2/3)(1/2)(1/1) = 12/120 = 1/10<br>
The general methods used by me and the other tutor are both very basic.  Again I state that you should know how to use both methods.<br>
If you are just learning about probability, I would recommend trying both methods on each problem.  Getting the same answer by two different methods gives you confidence that you are using the methods and doing the calculations correctly.