"90 students will graduate from Lima Shawness High..." was answered by our experts

Misael Sweeney

Answered question

2022-02-14

90 students will graduate from Lima Shawness High School this year. Out of the 90, 50 are planning to attend college. Two students are selected at to carry the flag at graduation. What is the probability that both of them are planning to attend college?

Answer & Explanation

Iacopelli5co

Beginner2022-02-15Added 15 answers

Step 1
We can divide the number of ways to select 2 from a pool of 90 (the entire graduating class) by the number of ways to select 2 from a pool of 50 (the members of the graduating class going to college).
We'll be using the combinations formula because we don't care in what order the two people are picked:
$C_{n, k} = \frac{n!}{(k!) (n - k!)}$ with $n = population, k = picks$
And so:
$\frac{C_{50, 2}}{C_{90, 2}} = \frac{\frac{50!}{2! 48!}}{\frac{90!}{2! 88!}} \Rightarrow$
$\Rightarrow \frac{50!}{⧸ 2! 48!} \frac{⧸ 2! 88!}{90!} \Rightarrow$
$\Rightarrow \frac{50 \times 49 \times ⧸ 48!}{⧸ 48!} \frac{⧸ 88!}{⧸ 88! \times 89 \times 90} \Rightarrow$
$\Rightarrow \frac{2450}{8010} \tilde{=} 0.306$
And so:
$P (picking 2 people as flag bearers who are also going on to college) = \frac{2450}{8010}$
$\tilde{=} 0.306$

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