Flag: suggested answer (don't read if don't want to see a (possibly incorrect) attempt:

Update - realise some bi-modal continuous distribution may be better (but potentially difficult to perform the update)

Attempt: we model the parameter pi in a Bayesian way: we put a distribution on pi (0.7 w.p 1/2, 0.2 w.p 1/2) then we weight the 1/2 with the likelihood of the observations, given that parameter (i.e. what is the likleihood when pi = 0.7, multiply that by 1/2 then divide by the normalizing constant to get our new probability for pi = 0.7 (do the same for pi = 0.2, the normalizing constant is the sum of the 'scores' for 0.7 and 0.2 i.e. 1/2 * likelihood so we can't 'divide by the normalising constant until we have the score for both 0.2 and 0.7)