<p>A bag contains $3$ blue counters, $1$ red counter and $y$ yellow counters. Darvina chooses $3$ counters at random from the bag, without replacement. The random variable $S$ is the sum of the numbers of blue counters chosen and twice the number of red counters chosen.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Show that $\mathrm{P}\left( S=3 \right)=\frac{6\left( 3y+1 \right)}{\left( y+4 \right)\left( y+3 \right)\left( y+2 \right)}$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Given that $\mathrm{P}\left( S=3 \right)=\frac{7}{20}$, calculate $y$. Hence find the probability distribution of $S$.</div><p style="text-align: right;">[6]</p></li></ol>

A bag contains $3$ blue counters, $1$ red counter and $y$ yellow counters. Darvina chooses $3$ counters at random from the bag, without replacement. The random variable $S$ is the sum of the numbers of blue counters chosen and twice the number of red counters chosen.

Show that $\mathrm{P}\left( S=3 \right)=\frac{6\left( 3y+1 \right)}{\left( y+4 \right)\left( y+3 \right)\left( y+2 \right)}$.

Given that $\mathrm{P}\left( S=3 \right)=\frac{7}{20}$, calculate $y$. Hence find the probability distribution of $S$.

2017 Specimen Paper P2 Q8

2017 Specimen Paper P2 Q8

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