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  • The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2,3 or 5 is______.Option: 1 0.26

The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2,3 or 5 is______.

Option: 1

0.26


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Method -I:

  Number of integers in the set which are divisible by
2 \: or \: 3\: or \: 5=
\mathrm{n(2 \cup 3 \cup 5) =n(2)+n(3)+n(5)-n(2 \cap 3)}
                            \mathrm{ -n(3 \cap 5)-n(5 \cap 2)+n(2 \cap 3 \cap 5)}
                            \mathrm{ =50+33+20-16-10-6+3}
                             \mathrm{ =74} 
                               

\mathrm{ \therefore} The number of integers between 1 and 100 which are not divisible by 2 or 3 or \mathrm{ 5=n(\overline{2} \cap \overline{3} \cap \overline{5})}
                                                                                                                                     \mathrm{ =100-n(2 \cup 3 \cup 5) }
                                                                                                                                      \mathrm{ =100-74=26}
\mathrm{ \therefore}  Req. probability
\mathrm{ =\frac{26}{100}=0.26}

Method II.

Between 1 to 100, No. of integers divisibile by ' 2 ' = 50

Between 1 to 100 , No. of integers divisibile by '3' but not by ' 2 '\mathrm{ =17}
Between 1 to 100 , No. of integers divisibile by ' 5 ' but not \mathrm{2 \& 3=8}
So overall \mathrm{74(50+17+18)}  are divisible by 2,3 or 5
Hence, \mathrm{100-74=26} are not divisible by 2,3 or 5 so req. prob

\mathrm{=\frac{26}{100}=0.26}

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