Question
An integer is chosen between $0$ and $100$. What is the probability that it is:
- Divisible by $7$?
- Not divisible by 7?
✓
Answer
The number of integers between 0 and 100 is, $n(S)=99$
Let $E _1=$ Event of choosing an integer which is divisible by 7
$=$ Event of choosing an integer which is multiple of 7
$=\{7,14,21,28,35,42,49,56,63,70,77,84,91,98\}$
$\therefore$ $n(E_1) = 14$
$\therefore\ \ \text{P(E}_1)=\frac{\text{n(E}_1)}{\text{n(S)}}=\frac{14}{99}$
Let $E_2 =$ Event of choosing an integer which is not divisible by $7$
$\therefore$ $n(E_2) = n(S) - n(E_1)$
$= 99 - 14 = 85$
$\therefore\ \ \text{P(E}_2)=\frac{\text{n(E}_2)}{\text{n(S)}}=\frac{85}{99}$
Let $E _1=$ Event of choosing an integer which is divisible by 7
$=$ Event of choosing an integer which is multiple of 7
$=\{7,14,21,28,35,42,49,56,63,70,77,84,91,98\}$
$\therefore$ $n(E_1) = 14$
$\therefore\ \ \text{P(E}_1)=\frac{\text{n(E}_1)}{\text{n(S)}}=\frac{14}{99}$
Let $E_2 =$ Event of choosing an integer which is not divisible by $7$
$\therefore$ $n(E_2) = n(S) - n(E_1)$
$= 99 - 14 = 85$
$\therefore\ \ \text{P(E}_2)=\frac{\text{n(E}_2)}{\text{n(S)}}=\frac{85}{99}$
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