To find the probability that a number drawn from 1 to 40 is divisible by both 3 and 5, we need to determine the numbers that are divisible by both 3 and 5 within this range.
Numbers divisible by 3: 3, 6, 9, ... , 39 (every 3rd number starting from 3)
Numbers divisible by 5: 5, 10, 15, ... , 40 (every 5th number starting from 5)
To find numbers divisible by both 3 and 5, we need to find the numbers that appear in both lists. These numbers are multiples of both 3 and 5, which are multiples of their least common multiple, 15.
Numbers divisible by both 3 and 5 (divisible by 15): 15, 30
There are two numbers (15 and 30) that are divisible by both 3 and 5 in the range from 1 to 40.
Therefore, the probability of drawing a number divisible by both 3 and 5 is the number of favorable outcomes (2) divided by the total number of possible outcomes (40):
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 2 / 40
Probability = 1 / 20
So, the probability that the number drawn is divisible by 3 and 5 is 1/20.
