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# a women has 10 keys out of which one opens a lock.she tries the keys one after the another(keeping aside the failed ones) till she succeeds in opening the lock. what is the chance that the 7th key works??

Grade:10

## 1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
If the 7th key is correct, the first six are incorrect.
. .(and we don't care about the last three.)

So, we want:.no - no - no - no - no - no - yes.

The probability is:.$\frac{9}{10}\cdot\frac{8}{9}\cdot\frac{7}{8}\cdot \frac{6}{7}\cdot\frac{5}{6}\cdot \frac{1}{5}$

. .which reduces to:.$\frac{\rlap{/}9}{10}\cdot\frac{\rlap{/}8}{\rlap{/}9}\cdot\frac{\rlap{/}7}{\rlap{/}8}\cdot \frac{\rlap{/}6}{\rlap{/}7}\cdot\frac{\rlap{/}5}{\rlap{/}6}\cdot \frac{1}{\rlap{/}5} \;=\;\frac{1}{10}$
Thanks and Regards
Shaik Aasif
askIITians faculty

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