Answer:
P=633/800
Step-by-step explanation:
The total number of integers from 1 to 2400 is 2400.
As understand we are looking for the numbers which can be divided at least by one of the numbers 6 or 8. Lets call all integers which can be divided by 6 or by 8 " black" integers and others " white" integers.
For example 6 can be divided by 6, however can not be divided by 8. However it is divided by 6 so we have to 6 belongs to " black" untegers.
The number of integers which can be divided by 6 is
2400:6=400 (1st sheet of black integers)
The number of integers which can be divided by 8 is 2400:8=300 (2nd shhet of black numbers).
So total amount of " black" integers= 400+300=700. However some of these integers can be divided both as by 6 as by 8.
These integers heve been included as to sheet 1 as to sheet 2. ANother words these integers have been included twice. SO we have to find the
total number of such integers and deduct them from 700.
These are the integers as follows:
3*4*2=24
3*4*3=36
3*4*4=48
3*4*5=60
3*4*6=72 ...
So these is any integer from 1 to 2400 which can be divided by 12 but own 12.
The number of such integers is:
2400:12-1=200-1=199
So the number of black integers is 700-199=501
That means that the number of white integers is 2400-501 = 1899
The required probability is P=1899/2400=633/800
