An interview question: About Probability

Question

An interview question:

Given a function f(x) that 1/4 times returns 0, 3/4 times returns 1. Write a function g(x) using f(x) that 1/2 times returns 0, 1/2 times returns

Answer 1

Since each return of f() represents a 3/4 chance of TRUE, with some algebra we can just properly balance the odds. What we want is another function x() which returns a balancing probability of TRUE, so that

function g() {    
    return f() && x();
}

returns true 50% of the time.

So let's find the probability of x (p(x)), given p(f) and our desired total probability (1/2):

p(f) * p(x) =  1/2
3/4  * p(x) =  1/2
       p(x) = (1/2) / 3/4
       p(x) =  2/3

So x() should return TRUE with a probability of 2/3, since 2/3 * 3/4 = 6/12 = 1/2;

Thus the following should work for g():

function g() {
    return f() && (rand() < 2/3);
}