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

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

Commented by malwaan last updated on 06/Jul/19

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

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