Question

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

• A. $\frac{33}{100}$
• B. $\frac{7}{100}$
• C. $\frac{4}{100}$
• D. $\frac{8}{100}$

Answer 1

The correct option is D $\frac{8}{100}$

Given: Numbers from $1$ to $100$

To find the probability that it is divisible by $4$ and $6$

According to the question, $n\left(S\right)=100$

Let A: be the event of numbers divisible by $4$ between $1$ to $100$

Then favourable outcomes of event $A$ are $\{4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100\}=25$

And $B$ be the event of numbers divisible by $6$ between $1$ to $100$

Then favourable outcomes of event $B$ are $\{6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96\}=16$

Hence the favourable outcomes for $4$ and $6$ are $\{12,24,36,48,60,72,84,96\},$ $n(A\cap B)=8$

Hence the probability of number divisible by $4$ and $6$ is $\frac{8}{100}$