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You are a member of a class of 18 Students.. A bowl contains 18 Chips, 2 Blue and 16 Red. Each student is to take 1 chip from the bowl without replacement. The student who draws the blue chip wins. Should you choose to draw first or fifth?

P(Blue on First)=2/18 P(Blue on Fifth)=P(Red and Red and Red and Red and Blue) = 16/18*15/17*14/16*13/15*2/14 =.08497

The correct answer is that probability-wise it should not matter, and both options should have a probability of 2/18. Where am I going wrong with P(blue on fifth)?

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You are skipping cases with first blue chip on any 4 places.

For blue on fifth we have,

$\frac {16}{18} × \frac {15}{17} × \frac {14}{16} × \frac {13}{15} × \frac {2}{14} + 4 \left[ \frac {2}{18} × \frac {16}{17} × \frac {15}{16} × \frac {14}{15} × \frac {1}{14} \right]$

$= \frac {13}{153} + \frac {4}{153}$

$= \frac {1}{9}$ or $\frac {2}{18}$