Probability qn 1 Revision as of 12:04, 15 July 2014 by Arjun Suresh (talk | contribs) (diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is:

(a)<math>16/25</math> (b)<math>(9/10)^3</math> (c)<math>27/75</math> (d)<math>18/25</math>

Solution by Arjun Suresh

First digit can be chosen in $8$ ways from $1-9$ excluding $7$

Second digit can be chosen in $9$ ways from $0-9$ excluding $7$ and similarly the third digit in $9$ ways.

So, total no. of ways excluding $7$ = $8*9*9$

Total no. of ways including $7$ = $9 * 10 * 10$

So, ans = $(8*9*9)/(9*10*10) = 18/25$

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