2012 A-level H2 Mathematics (9740) Paper 2 Question 7 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Required probability =\frac{14! \times 2!}{15!} = \frac{2}{15}

(ii)
Taking complement,
Required probability = 1 - \frac{13!\times 3!}{15!} = \frac{34}{35}

(iii)
Required probability =\frac{12! \times 2! \times 3!}{15!} = \frac{2}{455}

(iv)
Required probability =\frac{12}{15} + \frac{1}{35} - \frac{2}{455} = \frac{43}{273}

(v)
Required probability =\frac{13! \times 2!}{14!} = \frac{1}{7}

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