Thread: probability on a set of numbers

Two numbers a and b, are randomly selected without replacement from the set {2,3,4,5,6}. What is the probability that the fraction a/b is less than 1 and can be expressed as a decimal? Express answer in a fraction.

My approach to this problem is:
totally there are 5 numbers and once a number is taken from the set, it is not put back. So with one selection(1/5), two numbers have gone and so, for the second 1/3 and what about the remaing one number. I am afraid my approach is totally wrong.

Please guide me.

Thanks,

Originally Posted by Ka9

Two numbers a and b, are randomly selected without replacement from the set {2,3,4,5,6}. What is the probability that the fraction a/b is less than 1 and can be expressed as a decimal? Express answer in a fraction.

My approach to this problem is:
totally there are 5 numbers and once a number is taken from the set, it is not put back. So with one selection(1/5), two numbers have gone and so, for the second 1/3 and what about the remaing one number. I am afraid my approach is totally wrong.

Please guide me.

Thanks,

are all less than 1.

In fact, you only need to select 2 f the 5 numbers to be able to form such a fraction.

Some of these cannot be expressed as a decimal..
For example...

with the 6 repeating indefinately.

How many more cannot be expressed as decimals?

they have given 5 numbers {2,3,4,5,6}

you take any pair (a,b) (that is select any 2 numbers)

if a/b>1 then b/a<1 (ex: if 6/4 >1 then 4/6 <1)

therefore no. of fraction less than 1 will be equal to no. of fraction more than 1, formed using the given numbers.

probability=1/2

2/3,2/6,4/6,5/6 are repeating indefinately.
Among 10 possible fractions, only 4 are repeating indefinately. So, naturally the perfect one's are 6 out of 10. So, the answer is 6/10 i.e 3/5

Correct me.

Yes,
if we can (which I have done) interpret the question as asking
"what is the probability of forming a non-repeating decimal which is <1".

Thanks for guiding me. Thanks a lot.