Whose probabilty is better and why??

Question

We have 2 randomly generated no.s A and B between 0 and 1.
We r given only B. and we have to tell weather B > A or B < A.

there r 2 approaches:
1. If B > .5, always say B>A otherwise B
2. Generate another random no. say C, now, if CA otherwise say B
Which approach has high probability to give correct answer and why?

'adder 86' u r analysis of second approach is good...but i think in approach 1, the P(B>=A)=B as said by 'helmut'.

But can u put more light on what will be probability of approach 1 averaged over the whole sample space.

Answer 1

1. there's a 50% chance B > A when B > .5

2. there's a 50% chance B > A.
There's a 50% chance B > C
There's a 50% chance C > A
It's tricky to work out which number is greater in this case.

Look at all 6 possibilities:

A > B > C
A > C > B
B > A > C
B > C > A
C > B > A
C > A > B

In 2/6 cases, B > C and B < A
In 2/6 cases, B < C and B < A
In the other 2 cases, you would be wrong to follow the advice given.

Therfor, the second system is more reliable since it gets 66.66% acuracy.

Answer 2

P(B>=A) = B
1. if B>0.5 the statement B>A will be correct 50% of the time or more.

2. p(B>A) does not change if you generate a number C. Only if 0.5