Find the probability that a number chosen at random between 1 and 100 is divisible by 2 and 7.
how many multiples of 14 are there between 1 and 100?
⌊100/14⌋ = 7
so, the probability that you pick one of them is 7/100
To find the probability that a number chosen at random between 1 and 100 is divisible by both 2 and 7, we need to determine the number of numbers that satisfy both conditions and divide it by the total number of possible outcomes.
Step 1: Count the numbers divisible by 2.
Between 1 and 100, there are 50 numbers divisible by 2 (since half the numbers from 1 to 100 are even).
Step 2: Count the numbers divisible by 7.
Between 1 and 100, there are 14 numbers divisible by 7 (you can count them or divide 100 by 7, disregarding the remainder).
Step 3: Find the numbers divisible by both 2 and 7.
To find the numbers divisible by both 2 and 7, we need to find the common multiples of 2 and 7. The common multiples are 14, 28, 42, 56, 70, 84, and 98. So there are 7 numbers divisible by both 2 and 7 between 1 and 100.
Step 4: Calculate the probability.
The total number of possible outcomes is 100 (since we are choosing a number between 1 and 100).
Therefore, the probability that a number chosen at random between 1 and 100 is divisible by both 2 and 7 is:
7 (numbers divisible by both 2 and 7) / 100 (total possible outcomes) = 7/100 = 0.07 or 7%.