Investigate whether the following two proposals for producing decimal random digits by casting two

six-sided dice are correct. Denote the number of spots shown by the respective die by P and Q, and

the decimal random digit by X.

(a) If P = 6, then ignore the cast. Otherwise: if Q is even, set X equal to P; if Q is odd, set X equal to

the last digit in P + 5.

(b) If P + Q < 3, then ignore the cast. Otherwise, set X equal to P + Q 3.

note: Explain with a valid reason.

Please ellaborate the solutions also for both the parts.