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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.

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Last updated date: 13th Jun 2024
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Answer
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Hint:
The probability of both getting selected means multiplying the events of each person whereas the probability of selecting only one at a time requires addition of the events of both the persons.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

Complete step by step solution:
Given:
The probability of Kamal’s selection is $\dfrac{1}{3}$
And, the probability of Kamal’s selection is $\dfrac{1}{5}$
Let P(A) be the probability of Kamal gets selected
$P(A) = \dfrac{1}{3}$
And, P(B) be the probability of Monika gets selected
$P(B) = \dfrac{1}{5}$
Now, the probability of both getting selected means Kamal and Monika both getting selected.
Therefore, \[P\left( {Both{\text{ }}get{\text{ }}selected} \right){\text{ }} = {\text{ }}P\left( A \right){\text{ }} \times P\left( B \right)\]
$ = \dfrac{1}{3} \times \dfrac{1}{5}$
$ = \dfrac{1}{{15}}$
Therefore, the P (Both getting selected) = $\dfrac{1}{{15}}$
One can also approach by choosing both cases individually and subtracting 1 from it that is
$\dfrac{8}{{15}} + \dfrac{8}{{15}} = \dfrac{{16}}{{15}}$
$\dfrac{{16}}{{15}} - 1 = \dfrac{1}{{15}}$ [Which is P (Both getting selected)]
Where,
$\dfrac{8}{{15}}$ is nothing but P(A) + P(B) and two times $\dfrac{8}{{15}}$ is the condition of choosing both one at a time and subtracting 1 means choosing both Kamal and Monika at same time.
But, approaching with the first method is advised here. The second method is less explanatory.

Note:
In this type of question students often get confused while finding the probability of both. They usually add the two instead of multiplying. Do not make this mistake. Just to simplify, remember AND means multiply and OR means addition.