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?

Answer 1

Hint:The probability of selecting an object from multiple objects is by ratio in which the selected object is divided from the total number of apples and then equating it with the value of the probability of selecting a rotten apple.

\[\dfrac{\text{Selected Item}}{\text{Total Items}}=\] Probability of selection.
where the selected items are the rotten apples from the total apples.

Complete step by step solution:
The total number of rotten apples from the heap is taken as \[x\].
The total number of apples contained in the heap is given as \[900\].

The probability of selection in this case is sampling probability where we divide the item we need out of a sample or total amount given to us. Hence, the probability of selection is given as:
\[\Rightarrow \dfrac{\text{Selected Item}}{\text{Total Items}}=\dfrac{x}{900}\]

The probability of selecting a rotten apple is \[0.18\]. Equating both of them we get the equation as:
\[\Rightarrow \dfrac{x}{900}=0.18\]
\[\Rightarrow x=0.18\times 900\]
\[\Rightarrow x=162\]

Note:There are many types of sampling methods like random sampling, Bernoulli sampling or stratified sampling. The probability we used here is that of random sampling where at random an object is picked from the heap and formed ratio to find the probability.