Suppose there is a loss function (0, a) defined by On the basis of an observation x you have to take action a 0

Suppose there is a loss function ℒ (0, a) defined by

On the basis of an observation x you have to take action a₀, a₁ or a₂. For what values of the posterior probabilities p₀ and p₁ of the hypotheses H₀ : θ ∈ Θ₀ and H₁ : θ∈ Θ₁ would you take each of the possible actions?

a2 0 10 3 10 3.