Question

# You are performing an experiment 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?

Solution

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While dealing with mutually exclusive events (where $P(A\;\tt{and}\;B)$ are the shared values., the probability of $A$ or $B$ can be calculated with the following formula:

$P(A\;\tt{or}\;B)=P(A)+P(B)-P(A\;\tt{and}\;B)$

The probability of a plant receiving visible light, ultraviolet light and both, are the following:

\begin{align*} P(\tt{visible})&=\dfrac{12}{30}=\dfrac{2}{5}\\ P(\tt{ultraviolet})&=\dfrac{15}{30}=\dfrac{1}{2}\\ P(\tt{both})&=\dfrac{6}{30}=\dfrac{1}{5}\\ \end{align*}

We just have to plug in these values into the aforementioned equation to calculate the probability.

$P(\tt{visible}\;\tt{or}\;\tt{ultraviolet})=\dfrac{2}{5}+\dfrac{1}{2}-\dfrac{1}{5}=\dfrac{7}{10}=0.7$

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