Here are two ways to define randomized response:

A. flip a coin with bias p P r0,1{2s (i.e., the probability of observing heads and tails are p and 1p, respectively). If the coin comes tails, report the truth. Otherwise lie.

B. flip a fair coin (i.e., the probability of observing heads and tails are both 0.5). If the coin comes heads, report the truth. If the coin comes tails, flip another coin with bias q (i.e., the probability of observing heads and tails are q and 1 q, respectively). If this second coin comes tails, return the truth. Otherwise lie.

What value of q (in terms of p) makes these two implementation equivalent. Please show work