Question

One number is to be chosen from numbers $1$ to $100,$ the probability that it is divisible by $4$ or $6$ is:

• A. $\frac{33}{100}$
• B. $\frac{7}{100}$
• C. $\frac{4}{100}$
• D. $\frac{43}{100}$

Answer 1

The correct option is A $\frac{33}{100}$

Total number of numbers $n\left(S\right)=100$

Numbers divisible be 4 between 1 to 100 are $\{4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100\}$

Number divisible by 6 between 1 to 100 are $\{6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96\}$

Hence numbers divisible by 4 or 6 between 1 to 100 are $\{4,6,8,12,16,18,20,24,28,30,32,36,40,42,44,48,52,54,56,60,64,66,68,72,76,78,80,84,88,90,92,96,100\}$, $n\left(E\right)=33$

Hence the probability that it is divisible by 3 or 7 is $\frac{n\left(E\right)}{n\left(S\right)}=\frac{33}{100}$