Question

# The probability of selecting a rotten apple randomly from a heap of 900 apples is $0.18$.What is the number of rotten apples in the heap?

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Hint:- Probability of selecting element of type A $= \dfrac{{{\text{Number of elements of type A}}}}{{{\text{Total number of elements }}}}$

As, we know that,
Probability of selecting a rotten apple from a heap is given by,
$\Rightarrow$Probability $= \dfrac{{{\text{Number of rotten apples}}}}{{{\text{Total number of apples}}}}$ ……………. (1)
As, we are given with the total number of apples,
And the probability of selecting rotten apples.
$\Rightarrow$Total numbers of apples in the heap $= 900$............(2)
$\Rightarrow$Probability of selecting a rotten apple from a heap $= 0.18$............. (3)
So, putting values of equation 2 and 3 in equation 1. We get,
$\Rightarrow 0.18 = \dfrac{{{\text{Number of rotten apples}}}}{{900}}$
On, cross-multiplying. We get,
Number of rotten apples $= 900*0.18 = 162$
$\Rightarrow$Hence, there are 162 rotten apples in a heap.

Note:- Whenever we came up with this type of problem then easiest and efficient way
is to use the basic formula of probability, that probability of occurring an event is
$\dfrac{{{\text{Number of that event}}}}{{{\text{Total number of events}}}}$. Because in most of the problems of probability we will
get the required answer by using this formula only.