An integer is chosen between 0 and 100 (inclusive). Probability it is (i) divisible by 7 (ii) not divisible by 7?
(i) \(\dfrac{15}{101}\), (ii) \(\dfrac{86}{101}\)
Step 1: Count the total number of integers between 0 and 100 (inclusive).
That means we are counting: 0, 1, 2, ..., 100. So, there are
\(101\) integers in total.
Step 2: Find how many of these are divisible by 7.
Numbers divisible by 7 are called multiples of 7: 0, 7, 14, 21, …, 98.
Let us check the largest multiple: \(98 = 7 \times 14\).
So, the multiples are from \(7 \times 0 = 0\) up to \(7 \times 14 = 98\).
That gives us \(15\) numbers in total (from 0 to 14 gives 15 multiples).
Step 3: Probability of choosing a number divisible by 7.
Probability = \(\dfrac{\text{favourable outcomes}}{\text{total outcomes}}\).
Here, favourable outcomes = 15, total outcomes = 101.
So, Probability = \(\dfrac{15}{101}\).
Step 4: Probability of choosing a number not divisible by 7.
Total numbers = 101, numbers divisible by 7 = 15.
So, numbers not divisible by 7 = \(101 - 15 = 86\).
Therefore, Probability = \(\dfrac{86}{101}\).
Final Answer:
(i) Divisible by 7 = \(\dfrac{15}{101}\)
(ii) Not divisible by 7 = \(\dfrac{86}{101}\)