| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2024 |
| Session | September |
| Marks | 8 |
| Topic | Combinations & Selection |
| Type | Probability of specific committee composition |
| Difficulty | Standard +0.3 Part (i) is a standard combinations probability question requiring calculation of P(0,1,2, or 3 girls) using binomial coefficients - straightforward but computational. Part (ii) requires setting up the inequality 2(n-1)!/n! < 0.1, which simplifies to 2/(n) < 0.1, giving n > 20 - this is a routine arrangement problem with a minor algebraic step. Both parts are slightly above average due to the multi-case calculation and inequality setup, but use standard techniques without novel insight. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems |
2.\\
(i) A team of 9 is chosen at random from a class consisting of 8 boys and 12 girls. Find the probability that the team contains no more than 3 girls.\\
(ii) A group of $n$ people, including Mr and Mrs Laplace, are arranged at random in a line. The probability that Mr and Mrs Laplace are placed next to each other is less than 0.1 . Find the smallest possible value of $n$.\\[0pt]
\\
\hfill \mbox{\textit{SPS SPS FM Statistics 2024 Q2 [8]}}