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