a math teacher is randomly distributing 15 rulers with centimeters labels and 10 rulers without centimeter labels. What si the probability that the first ruler she hands out will have centimeter labels and the second ruler will not have labels?

prob(first has centimetres on it, the second does not)

= (15/25)(10/24) = 1/4

Well, since the teacher is randomly distributing the rulers, we can assume that each ruler has an equal chance of being chosen.

So, for the first ruler, there are a total of 15 rulers with centimeter labels out of a total of 25 rulers. Therefore, the probability of the first ruler having centimeter labels is 15/25.

Now, for the second ruler, if the first ruler had centimeter labels, there would now be 14 rulers left with centimeter labels and 10 rulers without labels. So, the probability of the second ruler not having labels would be 10/24.

To find the probability of both events happening together, we multiply the probabilities of each event. Therefore, the probability of the first ruler having centimeter labels and the second ruler not having labels is (15/25) * (10/24) = 150/600 = 1/4.

So, the probability that the first ruler she hands out will have centimeter labels and the second ruler will not have labels is 1/4.

To find the probability, we need to calculate the probability of two independent events occurring one after the other.

Step 1: Find the probability of the first ruler having centimeter labels:
There are a total of 15 rulers with centimeter labels, and 25 rulers in total. So the probability of the first ruler having centimeter labels is: P(first ruler with centimeter labels) = 15/25.

Step 2: Find the probability of the second ruler not having labels:
After the first ruler is handed out, there are now 24 rulers remaining, with 10 of them being without centimeter labels. Therefore, the probability of the second ruler not having labels is: P(second ruler without labels) = 10/24.

Step 3: Find the overall probability:
To find the overall probability of both events occurring, we multiply the probabilities together because they are independent events. Therefore, the probability of the first ruler having centimeter labels and the second ruler not having labels is:

P(both events occur) = P(first ruler with centimeter labels) * P(second ruler without labels)
= (15/25) * (10/24)
= 150/600
= 1/4
= 0.25

So, the probability that the first ruler she hands out will have centimeter labels and the second ruler will not have labels is 0.25 or 25%.

To find the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.

The teacher is randomly distributing 15 rulers with centimeter labels and 10 rulers without centimeter labels.

For the first ruler, there are a total of 25 rulers to choose from, and 15 of them have centimeter labels. So, the probability of selecting a ruler with centimeter labels for the first pick is 15/25.

Now, for the second ruler, after the first ruler is picked and removed, there are 24 rulers left, and 10 of them do not have centimeter labels. So, the probability of selecting a ruler without centimeter labels for the second pick is 10/24.

To find the probability of both events happening, we multiply the probabilities of each event:

Probability = (15/25) * (10/24) = 150/600 = 1/4

Therefore, the probability that the first ruler will have centimeter labels and the second ruler will not have labels is 1/4.