A math teacher is randomly distributing 15 rulers with centimeter labels and 10 rulers without centimeter labels. What is the probability that the first ruler she hands out will have centimeter labels and the second ruler will not have labels.
Well, let's do some ruler probability math!
To find the probability of the first ruler having centimeter labels, we divide the number of rulers with centimeter labels (15) by the total number of rulers (15 + 10 = 25). So the probability is 15/25.
Now, for the second ruler not having labels, we divide the number of rulers without labels (10) by the remaining number of rulers (24, after the first one is handed out). So the probability is 10/24.
To find the probability of both of these events happening, we multiply the probabilities together. So the probability that the first ruler has centimeter labels and the second ruler doesn't have labels is (15/25) * (10/24).
But, hey, remember that probability is fun and can be simplified! In this case, we notice that both 15 and 24 can be divided by 3, so let's simplify: (15/25) * (10/24) = (5/5) * (10/8) = 1 * (5/8) = 5/8.
So, the probability that the first ruler will have centimeter labels and the second ruler will not have labels is 5/8.
To determine the probability, we need to find the ratio of the number of desirable outcomes to the total number of possible outcomes.
First, let's find the number of rulers with centimeter labels (Desirable Outcome) and the number of rulers without centimeter labels (Total Outcome).
Number of rulers with centimeter labels = 15
Number of rulers without centimeter labels = 10
Total number of rulers = Number of rulers with centimeter labels + Number of rulers without centimeter labels
Total number of rulers = 15 + 10 = 25
To find the probability of the first ruler having centimeter labels and the second ruler not having labels, we multiply the probability of each event occurring.
Probability of the first ruler with centimeter labels = (Desirable Outcome / Total Outcome)
Probability of the first ruler with centimeter labels = 15 / 25 = 3 / 5
Probability of the second ruler without centimeter labels = (Desirable Outcome / Total Outcome)
Probability of the second ruler without centimeter labels = 10 / 24 = 5 / 12
Therefore, the probability that the first ruler she hands out will have centimeter labels and the second ruler will not have labels is:
Probability = (Probability of the first ruler with centimeter labels) * (Probability of the second ruler without centimeter labels)
Probability = (3 / 5) * (5 / 12)
Simplifying the expression, we have:
Probability = 3/5 * 5/12 = 15/60 = 1/4
So, the probability is 1/4 or 0.25 or 25%.
To find the probability of this event, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of rulers = 15 (with centimeter labels) + 10 (without centimeter labels) = 25 rulers.
For the first ruler, the probability of it having centimeter labels is 15 out of 25 since there are 15 rulers with centimeter labels out of a total of 25 rulers.
After distributing the first ruler, there will be 24 rulers remaining, 14 of which have centimeter labels and 10 without centimeter labels.
For the second ruler, the probability of it not having labels is 10 out of 24 since there are 10 rulers without centimeter labels remaining out of a total of 24 rulers.
To find the probability of both events occurring, we multiply their individual probabilities:
Probability = (15/25) x (10/24) = 150/600 = 1/4 = 0.25
Therefore, the probability that the first ruler has centimeter labels and the second ruler does not have labels is 0.25 or 25%.
what is (15/25)(10/24) ?
I answered this before
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