Question

A lot consists of $12$ good pencils, $6$ with minor defects and $2$ with major defects. A pencil is chosen at random. The probability that this pencil is not defective is
A.$\dfrac{3}{5}$
B.$\dfrac{3}{{10}}$
C.$\dfrac{4}{5}$
D.$\dfrac{1}{2}$

Answer 1

Hint : The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

Complete step-by-step answer :
Random Experiment: A random experiment is a mechanism that produces a definite outcome that cannot be predicted with certainty.
Sample Space: The sample space associated with a random experiment is the set of all possible outcomes. An event is a subset of the sample space.
Event: An event E is said to occur on a particular trial of the experiment if the outcome observed is an element of the set E.
We know that Probability (event)
$= \dfrac{{Number\;of\;favourable\;outcomes}}{{Total\;number\;of\;outcomes}}$
Here in this situation there are a total $20$ pencils. Hence the sample space consists of $20$ pencils.
Total number of good pencils i.e. total number of non defective pencils $= 12$
Total number of pencils $= 20$
Therefore we get ,
Probability (event)
$= \dfrac{{Number\;of\;favourable\;outcomes}}{{Total\;number\;of\;outcomes}}$
Probability (non defective pencil) $= \dfrac{{12}}{{20}} = \dfrac{3}{5}$
Therefore option (A) is the correct answer .
So, the correct answer is “Option A”.

Note : The meaning of probability is basically the extent to which something is likely to happen. Remember about random experiment, sample space and favourable outcomes related to the given event. Probability of any event can be between 0 and 1 only. Probability of any event can never be greater than 1. Probability of any event can never be negative.