Question

An integer is chosen at random from the number ranging from \[1\]to \[50\]. What is the probability that the integer chosen is a multiple of \[2\]or \[3\] or \[10\]?

Answer 1

Hint:In this question they have to choose integer random from the number ranging from \[1\]to \[50\]. We have to find the probability that the integer chosen is a multiple of \[2\]or \[3\] or \[10\].By the definition of probability, we get, the probability of a certain event is ratio of favorable outcomes of an event to the total outcomes.To solve the problem, at first, we will find the number of favourable outcomes. Then we can calculate the required probability.

Complete step-by-step answer:
It is given that; an integer is chosen at random from the number ranging from \[1\]to \[50\]. We have to find the probability that the integer chosen is a multiple of \[2\]or \[3\] or \[10\].
The possible outcomes that the integers from \[1\]to \[50\] are:
 \[
  1,2,3,4,5,6,7,8,9,10, \\
  11,12,13,14,15,16,17,18,19,20, \\
  21,22,23,24,25,26,27,28,29,30, \\
  31,32,33,34,35,36,37,38,39,40, \\
  41,42,43,44,45,46,47,48,49,50 \\
 \]
Now, we will find the multiples of \[2\] or \[3\] or \[10\] are: \[
  2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24,26,27,28,30, \\
  32,33,34,36,38,39,40,42,44,45,48,50 \\
 \]
So, the number of favourable outcomes is \[32\].
${\text{Probability = }}\dfrac{{{\text{The number of wanted outcomes}}}}{{{\text{The number of possible outcomes}}}}$
Using the formula of probability we get,
So, the probability that the chosen integer is a multiple of \[2\] or \[3\] or \[10\] is \[\dfrac{{32}}{{50}}\].
Simplifying we get,
The probability that the chosen integer is a multiple of \[2\] or \[3\] or \[10\] is \[\dfrac{{16}}{{25}}\].

Note:Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. You use probability in daily life to make decisions when you don't know for sure what the outcome will be. Most of the time, you won't perform actual probability problems, but you'll use subjective probability to make judgment calls and determine the best course of action.