Question

Cards numbered $7$ to $40$ were put in a box. Poonam selects a card at random. What is the probability that Poonam selects a card which is a multiple of $7$ $?$

Answer 1

Hint : First we have to find the total number of cards put in a box. Then find the numbers multiple of $7$ and less than or equal to $40$ . Then the probability that Poonam selects a card which is a multiple of $7$ is the ratio between the number of cards which are multiple of $7$ and the total number of cards.

Complete step by step solution:
Probability means possibility. Which deals with the occurrence of a random event. The probability is defined as the possibility of an event to happen is equal to the ratio between the number of favourable outcomes and the total number of outcomes.
Given cards numbered $7$ to $40$ were put in a box. Hence there are a total of 34 cards in a box.
Since the number multiple of $7$ and less than or equal to $40$ is $7,14,21,28,35$ . Hence, the total number of cards which are multiple of $7$ is $5$ .
Suppose E be the event that Poonam selects a card which is multiple of $7$ .
$P(E) = \dfrac{{Number{\text{ }}of{\text{ }}cards{\text{ }}which{\text{ }}are{\text{ }}multiple{\text{ }}of\;7}}{{Total\;number\;of\;cards}}$
$\Rightarrow$ $P(E) = \dfrac{5}{{34}}$ .
So, the correct answer is “ $P(E) = \dfrac{5}{{34}}$ .”

Note : Note that sometimes learners get mistaken for “favourable outcome” with “desirable outcome”. Also, for any event A, 0 ≤ P(A) ≤ 1. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.