Question

The probability of getting a bad egg in a lot of 500 is 0.028, find the number of good eggs in the lot.

Answer 1

Hint: We will first let the number of bad eggs be $x$. Since, the probability is given, use the formula, \[{\text{probability = }}\dfrac{{{\text{number of favourable outcomes}}}}{{{\text{total number of outcomes}}}}\] to form an equation in $x$. We can then calculate the number of good eggs by subtracting the number of bad eggs from the total number of eggs.

Complete step-by-step answer:

Probability of an event is defined as the chance of that event taking place. Mathematically probability of an event is defined as the Number of favourable outcomes divided by the total number of outcomes.
We begin the question by letting the number of bad eggs be $x$.
Then from the formula of probability we know,\[{\text{probability = }}\dfrac{{{\text{number of favourable outcomes}}}}{{{\text{total number of outcomes}}}}\]
Therefore, by using the given probability of bad eggs which is 0.28, we get,
\[0.028 = \dfrac{x}{{500}}\]
On cross multiplying the expression we get,
\[0.028\left( {500} \right) = x\]
On multiplying, we get \[x = 14\]
Thus, the number of bad eggs is 14.
Now, we will find the total number of eggs by subtracting the number of bad eggs from the total number of eggs.
\[{\text{Good eggs}} = {\text{ total number of eggs}} - {\text{number of bad eggs}}\]
Good eggs= 500-14=486 eggs.
Hence, there are 486 good eggs in the lot.

Note:- This can alternatively be done by first calculating the probability of good eggs. Probability of good eggs=1- probability of bad eggs. Then, let the number of good eggs be $x$ and use the formula of probability \[{\text{probability = }}\dfrac{{{\text{number of favourable outcomes}}}}{{{\text{total number of outcomes}}}}\] to form an equation. Solve the equation to find the total number of good eggs.