# probability on a set of numbers

• Jan 6th 2011, 04:48 PM
Ka9
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.

Thanks,
• Jan 6th 2011, 04:57 PM
Quote:

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.

Thanks,

$\displaystyle \frac{a}{b}<1$

$\displaystyle \frac{2}{3},\;\frac{2}{4},\;\frac{2}{5},\;\frac{2} {6},\;\frac{3}{4},\;\frac{3}{5},\;\frac{3}{6},\;\f rac{4}{5},\;\frac{4}{6},\;\frac{5}{6}$

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...

$\displaystyle \frac{2}{3}=0.6............$ with the 6 repeating indefinately.

How many more cannot be expressed as decimals?
• Jan 7th 2011, 04:26 AM
saravananbs
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
• Jan 7th 2011, 04:45 AM
Ka9
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.
• Jan 7th 2011, 04:52 AM