The combinations on the lockers at the high school consist of three numbers, each ranging from 0-39. If a combination is chosen at random, what is the probability that the first two numbers are multiples of 9 and the third number is a multiple of 4?
The combinations on the lockers at the high school consist of three numbers, each ranging from 0 to 39. If a combination is chosen at random, what is the probability of the event that the first two numbers are each multiples of 8 and the third number is a multiple of 5.
To find the probability of the given event occurring, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The first two numbers being multiples of 9 means they can be either 0, 9, 18, 27, or 36. So, there are 5 options for the first two numbers.
The third number being a multiple of 4 means it can be 0, 4, 8, 12, 16, 20, 24, 28, 32, or 36. So, there are 10 options for the third number.
Since all three numbers are chosen independently, the total number of possible outcomes is 40 * 40 * 40 = 64,000 (each digit can take any of the 40 options).
Therefore, the probability of choosing a combination where the first two numbers are multiples of 9 and the third number is a multiple of 4 is:
Number of favorable outcomes / Total number of possible outcomes
= (5 options for the first two numbers) * (10 options for the third number) / (64,000 total options)
= 50 / 64,000
= 1 / 1,280
So, the probability is 1/1,280.
To find the probability of this event, we need to determine the number of favorable outcomes (combinations that meet the given condition) and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes.
Since the first two numbers need to be multiples of 9 and the third number needs to be a multiple of 4, we can calculate the number of favorable outcomes through multiplication.
The number of multiples of 9 in the range of 0 to 39 is (39 - 0) / 9 + 1 = 5.
The number of multiples of 4 in the range of 0 to 39 is (39 - 0) / 4 + 1 = 10.
Therefore, the number of favorable outcomes is 5 (for the first two numbers) * 10 (for the third number) = 50.
Step 2: Determine the total number of possible outcomes.
Since each number in the combination can range from 0 to 39, there are 40 choices for each of the three numbers.
Therefore, the total number of possible outcomes is 40 (for the first number) * 40 (for the second number) * 40 (for the third number) = 64,000.
Step 3: Calculate the probability.
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 50 / 64,000
Simplifying the fraction, we get:
Probability = 1 / 1,280
Hence, the probability that the first two numbers are multiples of 9 and the third number is a multiple of 4 is 1 in 1,280.
There are four multiples of 9 and 9 multiples of four between 0 and 39.
If each number is independently chosen from 0 to 39, the probability of what you describe is
4/39 x 4/39 x 9/39 = 144/55,319 = 0.002428
or about 1 in 412