Generate 1 and 0 with equal probability

Problem:
Given a function “f” in which 0 occurs with probability 0.4 and 1 occurs with probability 0.6. Using function “f” deduce a new function “f1” such that both 0 and 1 occurs with probability 0.5.

Solution:
Run the function f() two times. The possible outcomes are

00 with probability 0.4*0.4

11 with probability 0.6*0.6

01 with probability 0.4*0.6

10 with probability 0.6*0.4

Notice that the probabilities for 01 and 10 are the same. So create a new function f1() such that

f1():
   first = f()
   second = f()
   if (first == 0 and second == 0) or (first == 1 or second == 1):

      discard and run again
   else: 
      if first == 0 and second == 1: return 0
      else: return 1

Complexity:

time - O(1)
space - O(1)

Links and credits:
http://www.geeksforgeeks.org/amazon-interview-set-64-campus-sde/

Generate integer from 1 to 7 with equal probability

Problem:
Given a function foo() that returns integers from 1 to 5 with equal probability, write a function that returns integers from 1 to 7 with equal probability using foo() only. Minimize the number of calls to foo() method. Also, use of any other library function is not allowed and no floating point arithmetic allowed.

Solution:
If we somehow generate integers from 1 to a-multiple-of-7 (like 7, 14, 21, …) with equal probability, we can use modulo division by 7 followed by adding 1 to get the numbers from 1 to 7 with equal probability.

Consider

5*foo() + foo() - 5

This expression generates numbers 1..25 with equal probability. Now, if we only accept numbers 1..21 and return i%7+1, then we get numbers 1..7 with equal probability. If the above expression returns a number >= 22, then ignore it and run the procedure once again until a proper number is returned.

int my_rand() // returns 1 to 7 with equal probability
{
    int i;
    i = 5*foo() + foo() - 5;
    if (i < 22)
        return i%7 + 1;
    return my_rand();
}

Complexity:

time - O(1), but really unpredictable, depends on the behavior of foo()
space - O(1)

Links and credits:
http://www.careercup.com/question?id=22457666
http://www.geeksforgeeks.org/generate-integer-from-1-to-7-with-equal-probability/
ARRAY: http://stackoverflow.com/questions/137783/expand-a-random-range-from-15-to-17