bjt behaviour in saturation mode
Rule of Thumb is Ic/Ib can vary from 10 to 50 depending on Hfe but is de facto specified as Ic/Ib =10 at some Vce(sat) but for small currents can be used at Hfe=20 to 50 but ONLY IF hFE in linear zone is extremely high beta.  Diodes Inc perfected this and have hundreds of patents to describe their doping methods.

So safe for all temps is hFE=10 then Vce(sat) is low.

BUT since Vout is not specified, you can make any assumption you want for Vce(sat)

IF V1=5.7 then you have 5V/50k = 0.1mA and assuming Vce(sat) = small or say 0.2V then Ic=4.8V/2k ~ 2.4mA

thus your Ic/Ib=25 is close but depends on hFE being >>250 in linear region for 10% of hFE on my Rule of Thumb.

if you used V1=3.1V then  your assumption of Ic/Ib=2.4mA/48uA=50 and Vce(sat) would rise to some value.

My formula is compute Rce sat for 2.4mA from datasheet and call that ΔV/ΔI=Rce and use that loss as the rise in Vce during saturation where bulk resistance dominates.

Using the MMBT2907ALT3GOSTR


But if Ic was 500mA then Vce would be quite higher and and Ic/Ib must be lower