Bayesian Posterior with Two Binary Signals

A binary event $E \in \{0, 1\}$ has prior $P(E = 1) = 0.40$. You receive two independent analyst signals $S_1, S_2 \in \{0, 1\}$, each with the same accuracy: $P(S_i = 1 \mid E = 1) = 0.70, \quad P(S_i = 1 \mid E = 0) = 0.30$ The signals are conditionally independent given $E$. You observe $(S_1, S_2) = (1, 0)$. Compute the posterior probability $P(E = 1 \mid S_1 = 1, S_2 = 0)$.