Dist. of Predicted Probability (DPP)

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hist(rnorm(3000, m=.15, sd=.025), 20, col=rgb(0,1,0,.25), xlim=c(0,1),
     xlab="Y = 0 (3000:Green)  ||   Y = 1 (1000:Red)",
     main="Distribution of Predicted Probability (Y = 1)")
hist(rnorm(1000, m=.35, sd=.025), 20, col=rgb(1,0,0,.25), add=TRUE)
abline(v=0.5,col='lightgray')

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With the Distribution of Predicted Probability shown above :

• What are the Accuracy, Sensitivity, Specificity, and AUC (at default threshold)?

• Is it possible that that AUC, Accuracy, Sensitivity, and Specificity all become 100% ?

• Is it possible that that AUC, Accuracy, Sensitivity, and Specificity all become 0 ?

• Can you modify the codes to make them (the above 2 cases) happen?