Question

The probability that the 4th power of a positive integer ends in the digit 6 is.
(A) 10%
(B) 20%
(C) 25%
(D) 40%

Answer 1

Hint: Counting numbers/ Natural numbers along with 0 are called positive integers.
Probability of any event (E) $ = \dfrac{{number{\text{ }}of{\text{ }}favourable{\text{ }}outcomes}}{{total{\text{ }}number{\text{ }}of{\text{ }}equally{\text{ }}likely{\text{ }}possible{\text{ }}outcomes}}$

Complete step-by-step answer:
If our unit digit of any number is 0 then the 4th power will give ‘0’ as unit digit.

If our unit digit of any number is 1 then the 4th power will give ‘1’ as unit digit.
If our unit digit of any number is 2 then the 4th power will give ‘6’ as unit digit.
If our unit digit of any number is 3 then the 4th power will give ‘1’ as unit digit.
If our unit digit of any number is 4 then the 4th power will give ‘6’ as unit digit.
If our unit digit of any number is 5 then the 4th power will give ‘5’ as unit digit.
If our unit digit of any number is 6 then the 4th power will give ‘6’ as unit digit.
If our unit digit of any number is 7 then the 4th power will give ‘1’ as unit digit.
If our unit digit of any number is 8 then the 4th power will give ‘6’ as unit digit.
If our unit digit of any number is 9 then the 4th power will give ‘1’ as unit digit.
Here, the number of favourable outcomes are ‘4’ as unit digit ending with 2,4,6 and 8 will give ‘6’ at unit digit after 4th power.
Total number of outcomes are 10 (0,1,2,3,4,5,6,7,8,9).
Probability that the 4th power of a positive integer ends in the digit ‘6’:
\[ = \dfrac{4}{{10}} = \dfrac{2}{5}\]
Required percentage \[ = \dfrac{4}{{10}} \times 100 = 40\% \]
Option (D) is correct.

Note: In question, the options are in percent so we converted probability into percentage by multiplying it with 100. Student’s must know the terms like favourable outcomes and total number of outcomes.
Favourable outcomes are the number of outcomes favouring the given condition.