Question

$20$ cards are numbered from $1 - 20$. One card is drawn at random. What is the probability that the card drawn is
A. a multiple of $4$
B. not a multiple of $6$

Answer 1

Hint: In this question, find the number of favourable outcomes and divide it by the total number of outcomes in the given twenty cards.

Complete step-by-step answer:
The probability of an event in mathematics is a number between $0$and $1$ where, $0$ indicates impossibility of the event and $1$ indicates the possibility.
The probability is given between two or more events. The two events are said to be independent if and only if probability of event first is equal to probability of second event.
The event to which an event is likely to occur is defined as the ratio of the favourable outcomes to the total number of cases possible. There are total $20$ cards.
(A) Here, We know that the number of favourable outcomes for the multiple of $4$ is,
$4,8,12,16,20$
Therefore, the total number of outcomes are $5$
Similarly, the probability that the number on the card is multiple of $4$ is,
$
  {P_1}\left( E \right) = \dfrac{5}{{20}} \\
   = \dfrac{1}{4} \\
 $

(B) Now, the number of favourable outcomes for the card is not a multiple of $6$ is,
$1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,19,20$
Therefore, the total number of outcomes are $17$, so the probability for the number on the card not a multiple of $6$ is,
${P_2}\left( E \right) = \dfrac{{17}}{{20}}$

Note: The probability of an event is the ratio of the number of favorable outcomes and the total number of favorable outcomes. In finding the probability, always find the correct number of favourable outcomes from total outcomes and correct sample space to obtain the correct answer.