x is chosen at random from all integers between 1 and 20 inclusive. What is the probability that it is a multiple of 3?
Listing the multiples of 3 form 1 to 20:
3, 6, ...., 18
how many are there?
What is the prob ?
Well, let me just juggle some numbers here... Ah, got it! There are 6 multiples of 3 between 1 and 20, which are 3, 6, 9, 12, 15, and 18. And since there are a total of 20 integers to choose from, the probability of randomly selecting a multiple of 3 would be 6/20, or simplifying it down, 3/10. So, the probability is about as high as a clown walking a tightrope – not guaranteed, but definitely possible!
To find the probability that x is a multiple of 3, we need to count the number of integers between 1 and 20 (inclusive) that are multiples of 3 and divide it by the total number of integers between 1 and 20 (inclusive).
Step 1: Count the number of integers between 1 and 20 (inclusive) that are multiples of 3.
The multiples of 3 between 1 and 20 (inclusive) are: 3, 6, 9, 12, 15, 18.
So, there are 6 integers between 1 and 20 (inclusive) that are multiples of 3.
Step 2: Find the total number of integers between 1 and 20 (inclusive).
The total number of integers between 1 and 20 (inclusive) is 20.
Step 3: Calculate the probability.
The probability that x is a multiple of 3 is given by the formula:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
In this case, the number of favorable outcomes (integers that are multiples of 3) is 6, and the total number of possible outcomes (integers between 1 and 20 (inclusive)) is 20.
So, the probability that x is a multiple of 3 is:
Probability = 6 / 20 = 3 / 10 = 0.3
Therefore, the probability that x is a multiple of 3 is 0.3 or 30%.
To find the probability that a randomly chosen integer between 1 and 20 inclusive is a multiple of 3, you need to determine the number of multiples of 3 within that range and divide it by the total number of integers in the set.
First, let's find the number of multiples of 3 between 1 and 20. The multiples of 3 in this range are: 3, 6, 9, 12, 15, 18. So, there are 6 multiples of 3.
Next, let's find the total number of integers between 1 and 20 inclusive. The integers in this range are: 1, 2, 3, 4, ..., 20. So, there are 20 integers.
Now, we can calculate the probability by dividing the number of multiples of 3 by the total number of integers: P(multiple of 3) = 6 / 20 = 0.3.
Therefore, the probability that a randomly chosen integer from this set is a multiple of 3 is 0.3 or 30%.
There are 20 numbers
There are 6 multiples of 3
So, P(x=3k) = 6/20