Suppose that a factory produces coins whose bias θ follow a Beta distribution with parameters α=5 and β=10. If a random coin was chosen from the factory and tossed 100 times which resulted in 50 heads and 50 tails. What is the probability of coin being fair?
Prior : Beta(5,10)
Posterior : Beta(50+5,50+10)
Now coin being fair is θ=0.5, But the probability of point in pdf is 0. I think the answer to 'probability of coin being fair' is 0. But still confused.
Am I missing something?