Question

A box contains 8 slips of paper, which are numbered 0 to 7. If one slip of paper is drawn unseen, the probability of drawing a number greater than 4 is?
A) $\dfrac{0}{8}$
B) $\dfrac{1}{8}$
C) $\dfrac{1}{4}$
D) $\dfrac{3}{8}$

Answer 1

We are required to find the probability of drawing a number greater than 4. The probability of any event is defined as the chances of an event to occur. It describes how likely or unlikely is the occurrence of any given event. Here, we will find the number of favorable outcomes. Then we will substitute these values in the formula of probability to get the answer.
Formula Used: In this question, we will use the following formula ${\text{Probability of an event}} = \dfrac{{{\text{number of favorable outcomes}}}}{{{\text{total number of outcomes}}}}$.

Complete step by step solution:
We are given that a box contains 8 slips of paper, which are numbered 0 to 7.
Thus, all the outcomes will be 0, 1, 2, 3, 4, 5, 6, and 7. Hence, our total number of outcomes is 8.
We can see that there are only three numbers in the box greater than 4; these are 5, 6, and 7. Hence, the number of our favorable outcomes will be 3.
Now we will substitute 3 for the number of favorable outcomes, and 8 for the total number of outcomes in the formula for the probability. We will get,
${\text{Probability of an event}} = \dfrac{{{\text{number of favorable outcomes}}}}{{{\text{total number of outcomes}}}}$
${\text{Probability of drawing a 4}} = \dfrac{3}{8}$
Since the fraction obtained cannot be simplified further, so, the probability of drawing a number greater than 4 is $\dfrac{3}{8}$.

Since our answer matches with option (D), hence, it is the correct option.

Note:
The probability of any event is always between 0 and 1. 0 indicates the impossibility of any event, and 1 indicates the certainty of any event. As in the question, it is given that there are 8 slips, we might make a mistake by taking 5, 6, 7 and 8 as the numbers greater than 4. If we take these numbers, then the probability of getting numbers greater than 4 will be $\dfrac{4}{8}$ or $\dfrac{1}{2}$ which will be wrong. As the slips are numbered from 0 to 7, so there will be only three numbers greater than 4, that is, 5, 6, 7. We will not include 8 because the slips are numbered from 0 to 7 only.