Find the probability that a number chosen at random between 1 and 100 is divisible by 2 and 7.
To find the probability that a number chosen at random between 1 and 100 is divisible by both 2 and 7, we first need to determine how many numbers in that range are divisible by both 2 and 7.
Step 1: Determine the number of multiples of 2 between 1 and 100.
Every other number is divisible by 2, so we need to count the multiples of 2. We can do this by dividing the range size by the common difference, which is 2.
100 / 2 = 50
Step 2: Determine the number of multiples of 7 between 1 and 100.
We divide the range size by the common difference, which is 7.
100 / 7 = 14 remainder 2.
Since we want to find the numbers divisible by both 2 and 7, we need to find the common multiples of 2 and 7. This can be done by finding the least common multiple (LCM) of 2 and 7.
The LCM of 2 and 7 is 14.
Step 3: Determine the number of common multiples of 2 and 7 between 1 and 100.
We divide the range size by the LCM, which is 14.
100 / 14 = 7 remainder 2.
Therefore, we have 7 numbers (14, 28, 42, 56, 70, 84, 98) that are divisible by both 2 and 7 between 1 and 100.
Step 4: Calculate the probability.
The probability of selecting a number divisible by both 2 and 7 is given by the number of successful outcomes (7) divided by the total number of possible outcomes (100).
Probability = Number of successful outcomes / Total number of possible outcomes
Probability = 7 / 100
Probability = 0.07 or 7%
So, the probability that a number chosen at random between 1 and 100 is divisible by both 2 and 7 is 7%.