question_answer

An integer is chosen at random between 1 and 100. Find the probability that it is:

(i) divisible by 8.

(ii) not divisible by 8.

Answer:

Total numbers are 2, 3, 4, ........., 99

(i) Let E be the event of getting a number divisible by 8.

\[E=\{8,16,24,32,40,48,56,64,72,80,88,96\}\]

\[=12\]

\[P(E)=\frac{Favourable\,\,outcomes}{Total\,\,outcomes}\]

\[=\frac{12}{98}=0.1224\]

(ii) Let E? be the event of getting a number not divisible by 8.

Then,   \[P(E)=1-P(E)\]

\[=\text{ }1-0.1224\]

\[=0.8756\]