If you pick a number completely at random from the natural numbers between 1 and 42, find the probability that the number is a multiple of 3.
lets see: 3,6,9,12,15,looks like every third number. So 2/3 of them are not multilples, 1/3 is
Pr= 1/3
the prob. will be 1/3.
To find the probability that a number picked randomly from the natural numbers between 1 and 42 is a multiple of 3, we need to determine the total number of multiples of 3 in that range, as well as the total number of possible outcomes.
Step 1: Counting the number of multiples of 3 in the range
To find the number of multiples of 3 in the range 1 to 42, we can divide the largest number (42) by 3 and round down to the nearest integer. So, 42 รท 3 = 14. Therefore, there are 14 multiples of 3 between 1 and 42.
Step 2: Counting the total number of possible outcomes
In this case, the total number of possible outcomes is simply the number of natural numbers between 1 and 42, which is 42.
Step 3: Calculating the probability
Now, we can calculate the probability by dividing the number of favorable outcomes (multiples of 3) by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Therefore, the probability of picking a number that is a multiple of 3 is:
Probability = 14 (number of multiples of 3) / 42 (total number of possible outcomes) = 1/3
So, the probability that a number picked randomly from the natural numbers between 1 and 42 is a multiple of 3 is 1/3.