Compute specificity and sensitivity at certain thresholds
For threshold = $0.5$ we have:

Sensitivity = True Positive Rate   

= (number of points with label $1$ and $P(T = 1)\geq 0.5$) divided by (number of points with label $1$)    

= $\left|\{(1, 0.54), (1, 0.88), (1, 0.90)\}\right| / 4$ = $3/4$ = $0.75$

Specificity = 1 - False Positive Rate    

= 1 - (number of points with label $0$ and $P(T = 1)\geq 0.5$) divided by (number of points with label $0$)    

= $1 - \left|\{(0, 0.78)\}\right|/6$ =  $1 - 1/6$ = $0.833$