# Thread: BOS Trial 2012

1. ## BOS Trial 2012

Hi,
Would anyone be able to explain the solutuion to Q10 of the 2012 BOS Trial (https://thsconline.github.io/frenzy/...U%20Trials.pdf )

Thanks

2. ## Re: BOS Trial 2012

Use binomial probability to get an expression involving n and sub in the options to find which one is the closest

$Probability of rolling a particular number = \frac{1}{n} \\ \\ Probability of rolling a particular number exactly 2 times: \\ \binom{3}{2}\left ( \frac{1}{n} \right )^2 \left ( \frac{n-1}{n} \right ) = 0.02 \\ \\ \Rightarrow 150(n-1)=n^3 \\ clearly n=12 is the closest solution \Rightarrow D$

3. ## Re: BOS Trial 2012

Why don't we multiply the LHS by n since there are n choices for the particular number that is rolled exactly twice?

4. ## Re: BOS Trial 2012

Originally Posted by frog0101
Why don't we multiply the LHS by n since there are n choices for the particular number that is rolled exactly twice?
You are picking a particular value of n, not doing it for all values of n. So to make it a bit easier to understand, say that you will complete an experiment where a die is rolled 3 times and we will record the outcome of each roll. We wish to have the outcomes as being two 1's and one not 1. What is the probability of this occurring?

Hope this helps. Note you can also get the above by combinatorics.

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