Question

Two integers are chosen at random and multiplied. The probability that the product is an even integer is
A.$\dfrac{1}{2}$
B.$\dfrac{2}{3}$
C.$\dfrac{3}{4}$
D.$\dfrac{4}{5}$

Answer 1

Hint : Here the given question is based on the concept of probability. We have to find the probability of choosing a random two integers and their product is an even integer, to first find the possible multiple of integers. Then by using the definition of probability and on further simplification we get the required probability.

Complete step-by-step answer :
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 probability of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
$Probability of event to happen P\left( E \right) = \dfrac{{Number \;of \;favourable \;outcomes}}{{Total\; Number \;of \;outcomes}}$
Consider, the given question
Given that, the two integers are chosen at random. Then,
If both the integers are even, then the product is equal to an even integer.
If both the integers are odd, then the product is equal to an odd integer.
If the one integer is even and the other integer is odd, then the product is equal to an even integer.
There are a total of 3 cases, out of which two cases will produce even integers which is a favourable outcome.
By the definition of probability
$\Rightarrow \,\,\,\,\,P(even\,intger) = \dfrac{{number\,of\,favourable\,outcomes}}{{Total\,no\,of\,cases}}$
$\therefore \,\,\,\,\,P(even\,intger) = \dfrac{2}{3}$
Hence, the required probability is $\dfrac{2}{3}$.
Therefore, Option (B) is the correct answer.
So, the correct answer is “Option B”.

Note : The probability is a number of possible values, students must know the definition of probability.
Integer is any number including 0, positive numbers, and negative numbers except fractions.
Any integer that can be multiple or divided exactly by 2 is known as an even integer and Any integer which is not a multiple of 2 is known as an odd integer.