There are 40 tags numbered one through 40 in a bag. What is the propability that Glen will randomly pick a multiple of 5 and then a multiple of 9 without replacing the first tag?

Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40 = 8/40

After picking the 5, there are only 39 tags for the second draw = 9, 18, 27, 36 = 4/39

Probability of all/both events occurring is found by multiplying probabilities of the individual events.

8/40 * 4/39 = ?

5/195

4/195 is the answer

To find the probability of Glen randomly picking a multiple of 5 and then a multiple of 9 without replacing the first tag, we need to divide the number of favorable outcomes by the total number of possible outcomes.

Let's break this down into steps:

Step 1: Count the number of tags that are multiples of 5.
There are 40 tags in total, so to find the number of tags that are multiples of 5, we need to divide 40 by 5. This gives us 8 tags that are multiples of 5.

Step 2: Count the number of remaining tags that are multiples of 9.
Since the first tag is not replaced, we now have one less tag in the bag. So there are 39 remaining tags. To find the number of tags that are multiples of 9, we need to divide 39 by 9. This gives us 4 tags that are multiples of 9.

Step 3: Multiply the number of favorable outcomes.
To find the number of favorable outcomes where Glen picks a multiple of 5 and then a multiple of 9, we multiply the number of favorable outcomes at each step. In this case, we have 8 choices for the first tag and 4 choices for the second tag. So the number of favorable outcomes is 8 * 4 = 32.

Step 4: Calculate the total number of possible outcomes.
Since there are 40 tags in the bag, there are 40 choices for the first tag and 39 choices for the second tag. So the total number of possible outcomes is 40 * 39 = 1560.

Step 5: Calculate the probability.
Now, to find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 32 / 1560

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 4:
Probability = 8 / 390

Therefore, the probability that Glen will randomly pick a multiple of 5 and then a multiple of 9 without replacing the first tag is 8/390.