Question

The probability of getting the rotten egg from a lot of 400 eggs is 0.035. Find the number of rotten eggs in the lot.

Answer 1

Hint: First of all, consider the number of rotten eggs as a variable. Then find the probability of the event of getting rotten eggs. As probability of the event is given, we can find the number of rotten eggs by substituting the given data.

Complete step-by-step answer:
Let the number of rotten eggs be \[x\]
Given that total number of eggs = 400
Probability of getting rotten eggs = 0.035
Let \[E\] be the event of getting a rotten egg.
We know that the probability of an event \[E\] is given by \[P\left( E \right) = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}\]
By using this formula, we get
\[
   \Rightarrow 0.035 = \dfrac{x}{{400}} \\
   \Rightarrow x = 0.035\left( {400} \right) \\
  \therefore x = 14 \\
\]
Thus, the number of rotten eggs in the lot is 14.

Note: The probability of an event \[E\] is always greater than or equal to zero and less than or equal to one i.e., \[0 \leqslant P\left( E \right) \leqslant 1\]. The number of outcomes is always greater than the number of favourable outcomes.