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The probability that a number selected at random between 100 and 999 (both
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The probability that a number selected at random between $100$ and $999$ (both
inclusive) will not contain the digit 7 is:
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inclusive) will not contain the digit $7$ is:
  
(a)16/25 (b)(9/10)^3 (c)27/75 '''(d)18/25'''
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(a)<math>16/25</math> (b)<math>(9/10)^3</math> (c)<math>27/75</math> '''(d)<math>18/25</math>'''
  
===Solution===
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==={{Template:Author|Arjun Suresh|{{arjunweb}} }}===
  
First digit can be chosen in 8 ways from 1-9 excluding 7
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First digit can be chosen in $8$ ways from $1-9$ excluding $7$
Second digit in 9 ways from 0-9 excluding 7 and third digit also 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
 
  
{{Template:FB}}
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Second digit can be chosen in $9$ ways from $0-9$ excluding $7$ and similarly the third digit in $9$ ways.
  
[[Category:Probability]]
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So, total no. of ways excluding $7$ = $8*9*9$
 +
 
 +
Total no. of ways including $7$ = $9 * 10 * 10$
 +
 
 +
So, ans = $(8*9*9)/(9*10*10) = 18/25$
 +
 
 +
{{Template:FBD}}
 +
 
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[[Category: Non-GATE Questions from Probability]]

Latest revision as of 12:04, 15 July 2014

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

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

Solution[edit]

First digit can be chosen in 8 ways from 1-9 excluding 7
Second digit in 9 ways from 0-9 excluding 7 and third digit also 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