# 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?

Last updated date: 27th Mar 2023

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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.

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.

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