CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A four digit number (numbered from 0000 to 9999) is said to be lucky if sum of its first two digits is equal to the sum of its last two digits. If a four digit number is picked up at random, then find the probability that it is lucky number.


A
Required probability=0.067
loader
B
Required probability=0.077
loader
C
Required probability=0.167
loader
D
Required probability=0.177
loader

Solution

The correct option is A Required probability$$=0.067$$
A 4 digit number can be written as 
$$1000(a)+100(b)+10(c)+d$$
It is lucky if $$(a+b)=c+d=n$$ ...(i)
If n=0, total combination is 1.
If n=1 total combinations are 4
If n=2 total combinations are 9
:
:
Again if n=9 total combinations are 100
If n=10  total combinations are 81
and so on till the total combination is again 1.
Hence 
Total number of lucky numbers is 
$$=1^{2}+2^{2}+...10^{2}+9^{2}+8^{2}+...1^{2}$$
$$=2(1^{2}+2^{2}+....10^{2})-10^{2}$$
$$=670$$
Total numbers will be $$10000$$
Hence the required probability is 
$$=\dfrac{670}{10000}$$
$$=0.067$$

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image