## Related questions with answers

The Chess Club at Asiniboyne High School consists of 6 seniors and 11 juniors. Presently, the club president and the club secretary are both seniors. (They must be different people.) If the students were selected randomly for these offices, what is the probability both would be seniors?

a. Show how to find the answer to this question using the General Multiplication Rule for probability.

b. Show how to find the answer using the Multiplication Principle of Counting and the definition of probability.

Solution

VerifiedA. Solve for the probability of selecting $2$ seniors for the position of President and Secretary using the General Multiplication Rule for Probability given that there are $6$ seniors and $11$ juniors in a chess club.

Let event $A$ and $B$ be choosing a senior.

$\begin{aligned} P( A \ and \ B)&=P(A) \cdot P(B|A)\\ &=\frac{6}{17} \cdot \frac{5}{16}\\ &=\frac{30}{272}\\ &=\frac{15}{136} \ or \ \approx 0.1103 \ or \ 11.03\% \end{aligned}$

On event $A$ there is a total of $6$ senior out of $17$ students so the probability of event $A$ will be $\frac{6}{17}$. Since a senior is already chosen on event $A$, event $B$ given $A$ will be $\frac{5}{16}$. Therefore, the probability of choosing both seniors for the position is $\frac{15}{136} \ or \ \approx 0.1103 \ or \ 11.03\%$.

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