Find the probability that a number chosen at random between 1 and 100 is divisible by 2 and 7.
14, 28, 42, 56, 70, 84, 98
7/100
Thank you! :) that's what I got,is there any more work to it? Because its an 8 mark question!
To find the probability that a number chosen at random between 1 and 100 is divisible by both 2 and 7, we need to identify the count of numbers that satisfy this condition.
First, let's find the count of numbers divisible by 2. Every other number (starting from 2) is divisible by 2. So, there are 100/2 = 50 numbers divisible by 2 in the range from 1 to 100.
Next, let's find the count of numbers divisible by 7. We can determine this by dividing the last number (100) by 7 and rounding down to the nearest integer. So, there are 100/7 = 14 numbers divisible by 7 in the range from 1 to 100.
To find the count of numbers divisible by both 2 and 7, we need to find the numbers that are divisible by the least common multiple of 2 and 7, which is 14. So, there are 100/14 = 7 numbers divisible by both 2 and 7 in the range from 1 to 100.
Now, to find the probability, divide the count of numbers divisible by both 2 and 7 (7) by the total count of numbers from 1 to 100 (100). Therefore, the probability is 7/100 = 0.07 or 7%.