if a number is chosen at random from the integer 5-25 inclusive find the probability that the number is a multiple of 5 or 3
there are 21 numbers available.
Multiples of 3 or 5: 5,6,9,10,12,15,18,20,21,24,25 -- 11 in all
so, the probability is 11/21
It was great and understandable
To find the probability that a randomly chosen number from the integers 5-25 (inclusive) is a multiple of 5 or 3, we need to determine the total number of favorable outcomes (numbers that are multiples of 5 or 3) and the total number of possible outcomes (total number of integers in the given range).
Step 1: Determine the total number of possible outcomes
The range of integers from 5-25 inclusive contains 21 numbers (5, 6, 7, ..., 25). So, the total number of possible outcomes is 21.
Step 2: Determine the total number of favorable outcomes
To find the numbers that are multiples of 5 or 3, we need to identify the multiples of 5 and the multiples of 3 within the given range.
Multiples of 5 in the range 5-25: 5, 10, 15, 20, 25
(There are 5 multiples of 5 in the range.)
Multiples of 3 in the range 5-25: 6, 9, 12, 15, 18, 21, 24
(There are 7 multiples of 3 in the range.)
However, we need to be careful not to count the number 15 twice, as it is a multiple of both 5 and 3. Therefore, we count it only once.
So, the total number of favorable outcomes is 5 (multiples of 5) + 7 (multiples of 3) - 1 (overlap) = 11.
Step 3: Calculate the probability
The probability is the ratio of the total number of favorable outcomes to the total number of possible outcomes.
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 11 / 21
Simplifying the fraction, we find that the probability that a number chosen at random from the integers 5-25 (inclusive) is a multiple of 5 or 3 is:
Probability = 11/21 (or approximately 0.5238, when rounded to four decimal places)