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Question Number 63596 by Tawa1 last updated on 05/Jul/19

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 any 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 begins with a letter besides A  and O. How many surnames begins with that letter ?

$$\mathrm{The}\:\mathrm{surnames}\:\mathrm{of}\:\mathrm{40}\:\mathrm{students}\:\mathrm{in}\:\mathrm{a}\:\mathrm{class}\:\mathrm{were}\:\mathrm{arranged}\:\mathrm{in} \\ $$$$\mathrm{alphabetical}\:\mathrm{order}.\:\mathrm{16}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surnames}\:\mathrm{begin}\:\mathrm{with}\:\mathrm{O}\:\mathrm{while} \\ $$$$\mathrm{9}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surnames}\:\mathrm{begin}\:\mathrm{with}\:\mathrm{A}.\:\:\mathrm{14}\:\mathrm{of}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{alphabet}\:\mathrm{do}\:\mathrm{not}\:\mathrm{appear}\:\mathrm{as}\:\mathrm{the}\:\mathrm{first}\:\mathrm{letter}\:\mathrm{of}\:\mathrm{any}\:\mathrm{surname}. \\ $$$$ \\ $$$$\left(\mathrm{i}\right)\:\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{surname}\:\mathrm{of}\:\mathrm{a}\:\mathrm{child}\:\mathrm{picked} \\ $$$$\mathrm{at}\:\mathrm{random}\:\mathrm{from}\:\mathrm{the}\:\mathrm{class}\:\mathrm{begins}\:\mathrm{with}\:\mathrm{either}\:\mathrm{A}\:\mathrm{or}\:\mathrm{O} \\ $$$$\left(\mathrm{ii}\right)\:\:\mathrm{If}\:\mathrm{more}\:\mathrm{than}\:\mathrm{one}\:\mathrm{surname}\:\mathrm{begins}\:\mathrm{with}\:\mathrm{a}\:\mathrm{letter}\:\mathrm{besides}\:\mathrm{A} \\ $$$$\mathrm{and}\:\mathrm{O}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{surnames}\:\mathrm{begins}\:\mathrm{with}\:\mathrm{that}\:\mathrm{letter}\:? \\ $$$$ \\ $$

Commented by malwaan last updated on 06/Jul/19

(i) ((16)/(40)) + (9/(40)) = ((25)/(40)) = (5/8)

$$\left({i}\right)\:\frac{\mathrm{16}}{\mathrm{40}}\:+\:\frac{\mathrm{9}}{\mathrm{40}}\:=\:\frac{\mathrm{25}}{\mathrm{40}}\:=\:\frac{\mathrm{5}}{\mathrm{8}} \\ $$

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