Of all the names...

Probability Level pending

So my teacher is drawing names for presentations. I am in a class of 25 students. He draws the first name, not me... second name, not me... third name, not me... fourth name, oh, it's me! What is the probability that I got chosen when I did (versus being 3rd, 2nd, 5th, etc.)? Note that he didn't put any names back once drawn.

B o n u s : Bonus: What is the probability of being chosen at any given point out of n n possibilites? Explain why.

1 24 \frac{1}{24} 21 ! 25 ! \frac{21!}{25!} 1 303600 \frac{1}{303600} 1 25 \frac{1}{25}

Feathery Studio by Feathery Studio , 20, Canada

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1 solution

Feathery Studio
Jun 5, 2015

Since the denominator and numerator get reduced by 1 each time a name is drawn, I had a 24 25 \frac{24}{25} chance that I didn't get chosen during the first draw, a 23 24 \frac{23}{24} chance I didn't get chosen during the second draw, 22 23 \frac{22}{23} chance I wasn't chosen during the third draw and a 1 22 \frac{1}{22} chance I was chosen in the fourth draw. So the probability is:

24 25 × 23 24 × 22 23 × 1 22 = 24 × 23 × 22 × 1 25 × 24 × 23 × 22 = 1 25 \frac{24}{25}\times\frac{23}{24}\times\frac{22}{23}\times\frac{1}{22} = \frac{24\times23\times22\times1}{25\times24\times23\times22} = \boxed{\frac{1}{25}}

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