Question 1159039: The surname of 40 students in a class was arrange in alphabetical order.16 of the surnames begin with O while 9 of the surnames begin with A. 14 of the letters of the alphabet do not appear as the first letter of the surname.
i.what is the probability that the surname of a child picked at random from the class begins with either A or O?
ii.if more than one surname begin with a letter besides A and O, how many surnames begins with that letter?
Answer by ikleyn(54018)   (Show Source):
You can put this solution on YOUR website! .
The surname of 40 students in a class was arrange in alphabetical order. 16 of the surnames begin with O
while 9 of the surnames begin with A. 14 of the letters of the alphabet do not appear as the first letter of the
surname.
(i). what is the probability that the surname of a child picked at random from the class begins with either A or O?
(ii). if more than one surname begin with a letter besides A and O, how many surnames begins with that letter?
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The problem's formulation in the post is totally wrong and absolutely incorrect.
First, it is incorrect from an English grammar standpoint.
When I read it, it feels like I'm traveling in a car with square wheels.
What is even worse, in question (ii), it is incorrect from a common-sense mathematical standpoint,
which makes its solution impossible.
To fix the problem, in question (ii), it should be TOTALLY rewritten.
My correction (the corrected version) is below.
The surnames of 40 students in a class were arranged in alphabetical order. 16 of the surnames begin with O
while 9 of the surnames begin with A. 14 of the letters of the alphabet do not appear as the first letter of the
surname.
(i). What is the probability that the surname of a child picked at random from the class begins with either A or O?
(ii). If there is only one letter besides A and O, such that more than one surname begins with this letter,
how many surnames begin with that letter?
Below is my solution for this fixed/repaired/modified formulation.
Question (i) is very simple. The probability under this question is  =  =  .
Question (ii) in my modified formulation requires longer reasoning.
After excluding 16 students whose surnames start with A and excluding 9 students whose surnames start with O,
we have 40 - 16 - 9 -= 40 - 25 = 15 remaining students and 15 remaining surnames.
For them, we have 26 - 14 - 2 = 10 letters that really are the first letters of their surnames.
Of these 10 letters, only one is repeated, as given in the problem. The remaining 9 letters are unique.
Hence, the repeated letter appears 15 - 9 = 6 times as the first letter of surnames besides A and O.
At this point, the problem is solved completely.
ANSWER. How many surnames begin with that letter? 6 (six) surnames.
What I wrote in my post demonstrates the care required when dealing with mathematical problems.
One cannot entrust their formulation to non-professionals, as they will distort the meaning of the problem
beyond recognition — often without even realizing it.
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