Question

One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?

Answer 1

Let A be the event of choosing a number divisible by 4

$\therefore A=4,8,....,100$

$\Rightarrow n\left(A\right)=25$

$P\left(A\right)=\frac{25}{100}$

Let B be the event of choosing a number divisible by 6

$\therefore B=6,12,...,96$

$\Rightarrow n\left(B\right)=16$

$P\left(B\right)=\frac{16}{100}$

$(A\cap B)=12,24,.....,96$

$\Rightarrow n(A\cap B)=8$

$\therefore P(A\cap B)=\frac{8}{100}$

$\therefore P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

=$\frac{25}{100}+\frac{16}{100}-\frac{8}{100}=\frac{33}{100}$