Question

In an interview conducted for 5 ABC Consulting candidates, 6 Global Ltd. candidates, 2 candidates from Avilvar company, 3 from Sona Ltd and one from Bent company, what is the probability that the candidate who would be selected is from Sona Ltd. (It is given that one candidate from Global Ltd. had not come for the interview round and one candidate from ABC Consulting got blacklisted during the interview process.​)

Answer 1

Hint: Here the given question is based on the concept of probability. We have to find the probability of choosing a candidate from Sona Ltd. So we write the given data in the numeral form and by definition of probability we write the solution for the given question.

Complete step by step solution:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it. Probability can range in from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
\[Probability \;of \;event \;to \;happen \;P\left( E \right) = \dfrac{{Number \;of \;favourable \;outcomes}}{{Total \;Number \;of \;outcomes}}\]
Now consider the given question and we write the given data, so we have
Number of candidates from ABC consulting = 5
Number of candidates from Global Ltd = 6
Number of candidates from Avilvar company = 2
Number of candidates from Sona Ltd = 3
Number of candidates from Bent company = 1
Then the number of candidates who have attended interview = 17
The number of candidates who have not attended interview = 2.
Now the total number of candidates who have attended the interview = 17 – 2 = 15
The 15 represents the total number of outcomes.
Here we have to find the probability that we are selecting the candidates from Sona Ltd.
The number of candidates selected from Sona Ltd = 3
 Let E represents the event where we select a candidate from Sona Ltd.
The number of favourable outcomes = 3
The total number of outcomes = 15
The probability of event E is written as
\[P\left( E \right) = \dfrac{3}{{15}}\]
On simplifying we have
\[ \Rightarrow P\left( E \right) = \dfrac{1}{5}\]
The probability that the candidate who would be selected is from Sona Ltd. is \[\dfrac{1}{5}\]
So, the correct answer is “ \[\dfrac{1}{5}\]”.

Note: The probability is a number of possible values. Candidate must know we have to use the permutation concept or combination concept to solve the given problem because it is the first and main thing to solve the problem. Here we arrange the things in the possible ways so we are using the concept permutation.