Question

A sample of 3 bulbs is tested. A bulb is labelled as G if it is good and D if it is defective. Find the number of all possible outcomes.

Answer 1

Hint:For solving this question, first we will see the concept of the fundamental principle of multiplication. After that, we will find the number of choices available for each bulb when we test it separately. Then, we will multiply all the number of choices to get the final answer.

Complete step-by-step answer:
It is given that there is a sample of 3 bulbs which is going to be tested. A bulb is labelled as G if it is good and D if it is defective. And we have to find the total number of possible outcomes.
Now, before we proceed we should know the following important concept and formulas:
Fundamental Principle of Multiplication:
If there are two jobs such that one of them can be completed in $m$ ways, and when it has been completed in any of these $m$ ways, the second job can be completed in $n$ ways. Then, two jobs in succession can be completed in $m\times n$ ways.
 Now, as it is given that, when a bulb is tested, then it is labelled as G if it is good and D if it is defective. Which means, every bulb has $2$ choices only and i.e. to be labelled as G if it is good and D if it is defective.
Now, let ${{b}_{1}},{{b}_{2}},{{b}_{3}}$ are the three bulbs which are going to be tested.
Now, we will find the number of choices available for each bulb when we test it separately.
The number of choices available for the bulb ${{b}_{1}}=2$ choices.
The number of choices available for the bulb ${{b}_{2}}=2$ choices.
The number of choices available for the bulb ${{b}_{3}}=2$ choices.
Now, from the fundamental principle of multiplication, we can say that the total number of all possible outcomes will be equal to $2\times 2\times 2=8$ ways.
Thus, the total number of possible outcomes will be equal to $8$ ways.

Note:Here, the student should first understand what is asked in the question and then proceed in the right direction to get the correct answer quickly. After that, we should apply the fundamental principle of counting very carefully. Moreover, as there are 3 bulbs and they have only 2 choices so, we could have directly used the formula ${{2}^{n}}$ to get the total number of possible outcomes with the value of $n=3$ .