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  • Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is probability that the selected number is not divisible by 7 ?  <div class='q

Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is probability that the selected number is not divisible by 7 ?
 

Option: 1

\frac{13}{90}


Option: 2

\frac{12}{90}


Option: 3

\frac{78}{90}


Option: 4

\frac{77}{90}


Answers (1)

best_answer

Two digit numbers divisible by 7 are \left \{ 14,21,28, \ldots 91. 98 \right \}

Last term,\mathrm{I =a+(n-1) d }

\mathrm{98 =14+(n-1) 7 }

\mathrm{\frac{84}{7} =(n-1) }

\mathrm{n =13 .}

There are 13 two digit numbers divisible by 7 . Therefore out of 90 two digits numbers 77 are not divisible by \mathrm{7(\because 90-13=77)}

\therefore The required probability,

\mathrm{ P(E)=\frac{77}{90} }
 

Posted by

vishal kumar

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