Question

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 1

Hint: First of all, we will calculate the total outcomes of the given probability. Then, we will list all the numbers divisible by 8. We will use the definition of the probability to calculate the probability that the integer is divisible by 8. After that, for calculating the probability that the integer is not divisible by 8, we will use the formula:
Probability of not being divisible by 8 = 1 – probability of being divisible by 8

Complete step-by-step answer:
The total of integers between 1 and 100 is: 2, 3, 4, ….., 99 = 98
Therefore, the total outcomes = 98.
The numbers between 1 and 100 which are divisible by 8 can be listed as:
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
Hence, the total number of possible outcomes = 12
Now, the definition of probability is that the probability is a measure of occurrence of a random event. It can be defined as: probability = $\dfrac{{{\text{possible outcomes}}}}{{{\text{total outcomes}}}}$
Therefore, the probability that the integer chosen is divisible by 8 can be given by:
$ \Rightarrow P({\text{divisible by 8}}) = \dfrac{{12}}{{98}} = \dfrac{6}{{49}}$
Now, we have calculated the probability of an integer divisible by 8. For the probability of the chosen integer which is not divisible by 8, we will use the formula:
$ \Rightarrow $Probability (divisible by 8) + probability (not divisible by 8) = 1
$ \Rightarrow $ Probability (not divisible by 8) = 1 – probability (divisible by 8)
$ \Rightarrow $ Probability (not divisible by 8) = 1 – $\dfrac{6}{{49}}$ = $\dfrac{{43}}{{49}}$
Therefore, I) probability (divisible by 8) is $\dfrac{6}{{49}}$
II)probability (not divisible by 8) is $\dfrac{{43}}{{49}}$.

Note: In this question, remember divisibility rule of 8 and probability formula. You can also solve the probability (not divisible by 8) by subtracting 12 (outcomes of the integers divisible by 8) from the total outcomes and then using the definition of the probability to calculate the probability.