Correcting The Counts

Single-qubit readout calibration on a device:

prepared	measured 0	measured 1
$\lvert 0\rangle$	0.97	0.03
$\lvert 1\rangle$	0.08	0.92

You run a circuit for 10,000 shots and observe 4,000 counts of 1.

Treating the observed distribution as $A,p_{\text{true}}$ with $A = \begin{pmatrix} 0.97 & 0.08 \ 0.03 & 0.92 \end{pmatrix}$ , what is the corrected estimate of $P(1)$ ?

$0.370$

$\approx 0.416$

$0.400$

$\approx 0.435$