You perform an experiment for your science project to determine how well plants grow under different light sources. Of the 30 plants in the experiment, 12 receive visible light, 15 receive ultraviolet light, and 6 receive both visible and ultraviolet light. What is the probability that a plant in the experiment receives visible or ultraviolet light? Express your first answer as a simplified fraction.The probability that a plant receives visible or ultraviolet light is , or %
Question
You perform an experiment for your science project to determine how well plants grow under different light sources. Of the 30 plants in the experiment, 12 receive visible light, 15 receive ultraviolet light, and 6 receive both visible and ultraviolet light. What is the probability that a plant in the experiment receives visible or ultraviolet light? Express your first answer as a simplified fraction.The probability that a plant receives visible or ultraviolet light is , or %
Solution
To calculate the probability that a plant receives either visible or ultraviolet light, we first need to determine the total number of plants that receive either of these types of light.
From the problem, we know that 12 plants receive visible light, 15 plants receive ultraviolet light, and 6 plants receive both. However, we don't want to double count the plants that receive both types of light, so we subtract those from the total.
So, the total number of plants that receive either visible or ultraviolet light is 12 (visible) + 15 (ultraviolet) - 6 (both) = 21 plants.
The total number of plants in the experiment is 30.
Therefore, the probability that a plant receives either visible or ultraviolet light is the number of plants that receive either type of light divided by the total number of plants.
So, the probability is 21/30.
To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 3.
So, the simplified fraction is 7/10.
To express this as a percentage, we multiply the fraction by 100.
So, the probability that a plant receives either visible or ultraviolet light is 7/10, or 70%.
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