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 find the probability of drawing a number greater than 4 by dividing the favorable outcomes by total number of outcomes. Count the numbers that are greater than 4 and then find the probability of drawing those numbers.

Complete step-by-step answer:
We have total number of slips as 8
So, total number of observations is 8
Numbers on the slips are 0, 1, 2, 3, 4, 5, 6 and 7
We have to find a probability of drawing a slip that has a number greater than 4.
The numbers from the list of slips that are greater than 4 are 5, 6 and 7
So, there are three favorable outcomes
Use the formula for probability of an event.
Probability of drawing a number greater than 4 is equal to numbers greater than 4 on slips divided by total number of slips
Probability $= \dfrac{3}{8}$

So, the correct option is D.

Note: Alternate method:
We can find probabilities of each number greater than 4 to be drawn separately.
Total number of slips is 8.
Numbers greater than 4 are 5, 6 and 7
Probability of drawing 5 from 8 slips is $\dfrac{1}{8}$
Probability of drawing 6 from 8 slips is $\dfrac{1}{8}$
Probability of drawing 7 from 8 slips is $\dfrac{1}{8}$
Therefore, the probability of drawing one slip from 5, 6 and 7 is the sum of the probabilities of each number on the slip individually.
Probability $= \dfrac{1}{8} + \dfrac{1}{8} + \dfrac{1}{8}$
Take LCM
$\Rightarrow$Probability $= \dfrac{{1 + 1 + 1}}{8}$
$\Rightarrow$Probability $= \dfrac{3}{8}$
So, the correct option is D.