Question

Kamal and Monika appeared for an interview for two vacancies. The probability of Kamal's selection is $ \dfrac{1}{3} $ and that of Monika's selection is $ \dfrac{1}{5} $ . Find the probability that both of them will be selected.

Answer 1

Hint: In this question, we need to determine the probability that both Kamal and Monika will be selected in the interview for the two vacancies. For this, we will follow the concept of the independent events.

Complete step-by-step answer:
The probability of the selection of Karan for the vacancies in the interview is $ \dfrac{1}{3} $ .
The probability of the selection of Karan for the vacancies in the interview is $ \dfrac{1}{5} $ .
The probability of the two independent events is the product of the probability of the individual events. Mathematically, $ P\left( {A \cap B} \right) = P\left( A \right)P\left( B \right) $ where, A and B are two independent events.
As the total number of vacancies are two and here we are dealing with the two candidates only so, their individual selection is completely independent of one other i.e., selection of either candidate Karan or Monika will not affect the selection of the other.
Here, in the question, the two independent events are selection of Karan and Monika. So,
  $ P(A) = \dfrac{1}{3} $ and $ P(B) = \dfrac{1}{5} $
So, the probability of selection of both candidates (Karan and Monika) is given as:
  $
\Rightarrow P\left( {A \cap B} \right) = P\left( A \right)P\left( B \right) \\
   = \dfrac{1}{3} \times \dfrac{1}{{15}} \\
   = \dfrac{1}{{15}} \\
   $
Hence, the probability that both of them will be selected is $ \dfrac{1}{{15}} $ .

Note: It is interesting to note that in the question, it is asked for the probability of selection of both candidates, if the question asks for the selection of either then, we will evaluate the probability of the rejection of the candidates and then, carry forward our calculation in the same way.