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# During the Holi festival, Sonali filled 7 bottles with different colored water – red, blue, green, pink, yellow, purple, and orange. One bottle is selected at random. What is the probability of selecting the bottle with brown color?

Last updated date: 22nd Jul 2024
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Hint: When we select a colored bottle then it is equally likely that any bottle can come. We know the formula for the probability of any desired outcome is equal to $\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$. Now, total outcomes are 7 because any color bottle can be picked up at random and the favorable outcome is the bottle of brown color so the number of favorable outcomes is 1. Substituting these values in the given formula will give the required probability.

Complete step-by-step solution:
In the above problem, we have given 7 bottles with different colors and we have selected one of the bottles at random. Selecting a bottle and getting any colored bottle is equally likely.
We know the formula for the probability which is equal to:
$\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$
Now, the total outcomes could be 7 because when we select a bottle at random then the total number of bottles from which we have to select one bottle is 7.
And the number of favorable outcomes is 1 because we require a brown-colored bottle and amongst 7 bottles, one of the bottles is a brown colored bottle.
Substituting the value of favorable outcome as 1 and total outcomes as 7 in the above probability formula we get,
\begin{align} & \dfrac{\text{Favorable outcomes}}{\text{Total outcomes}} \\ & =\dfrac{1}{7} \\ \end{align}
From the above solution, the probability of selecting the bottle with brown color is $\dfrac{1}{7}$.

Note: To solve the above problem, you must know the formula to find the probability of any favorable outcome. The mistake that could be possible in the above problem is that you might write “brown” in place of favorable outcomes which is completely a wrong thing. So, do remember that probability is a number that lies from 0 to 1.