Q$\mathrm{.}3$: Consider the given dataset, build a binary logistic regression model to predict the likelihood of a customer purchasing the product based on their demographic information $($age$,$ income, gender$).$ Interpret the coefficients and predict the probability of a $35-$year$-$old male with an income of $$50,000$ purchasing the product.

$\backslash$table$[[$Age$,$Income $($$$1000$s$),$Gender,Purchased $(1/0)],[25,35,$Male,$1],[30,50,$Female,$0],[35,45,$Male,$1],[40,60,$Female,$1],[45,55,$Male,$0],[50,70,$Female,$1]]$