The bias of a coin (i.e., the probability of Heads) can take three possible values, 1/4 , 1/2 , or 3/4 , and is modeled as a discrete random variable Q with PMF

Question

pQ(q)=⎧⎩⎨⎪⎪⎪⎪⎪⎪1/6,2/6,3/6,0,if q=1/4,if q=2/4,if q=3/4,otherwise.

Let K be the total number of Heads in two independent tosses of the coin. Find pQ|K(3/4|2) .

Answer 1

3/8

Answer 2

Luli's answer is wrong

Answer 3

3/4