Yes, transistor are Q1-ON; Q2-OFF; Q3-ON or if we have a switch in B position we have
Q1-OFF; Q2-ON; Q3-OFF
Do you know what "short" is in electronic ?
Read this
https://www.physicsforums.com/attachment.php?attachmentid=65135&d=1388163392
We can also say that: Q2 is CUT_OFF because Q1 transistor collector-emitter saturation voltage (Vce(sat)) is lower then 0.6V needed to TURN ON Q2. And this is why Q2 is CUT-OFF. No, Q2 is OFF but current will still flow through BL2 so the bulb will glow.
Haven't you noticed that when Q2 is OFF, the Q3 base current will now flow through the bulb?
Because you forget that base current also flow through the light bulb.
And if this base current is large (low resistance) the light bulb will glow.
In circuits when transistor work as a switch (transistor is in saturation region of in cut-off) we can easily calculate all current in the circuit. All we need to know is the resistance and Vcc voltage.
The base current is equal to:
Ib = (Vcc - Vbe)/Rb where:
Vcc --> power supply voltage
Vbe --> Base-emitter diode forward voltage drop (0.6V ... 0.8V)
RB --> base resistor resistance in our circuit Rb is 1K for Q1 base and for the rest of a transistors RB = light bulb resistance.
And collector current is equal to
Ic = (Vcc - Vce(sat))/Rc
Vce(sat) - Collector-emitter saturation voltage (0.2V typical).
Rc --> resistance connect between Vcc and collector in our case light bulb resistance.
Are you sure that current is zero for second bulb (BL2)? You still forgetting about base current.
Once more take a look at this
As you can see we have a switch in A position. So Q1 is ON ; Q2 is OFF and Q3 is ON.
And second bulb glows, because Q3 transistor base current is now flowing through the light bulb. The Q3 base current is mark in green on the diagram. Because now despite the fact that Q1 is OFF the BL1 current is not equal to 0A.
As you can see here in red
Q2 transistor base current is now flow through first light bulb.
Additional the light bulb resistance is ""low" so the base current is high:
Ib = (10V - 0.7V)/100Ω ≈ 93mA and this is why light bulb glow (shines). But everything work as is should be. And to fix this issue with the bulbs simple reduce the base current. Can you tell me the name of the book you are reading now?
try this books
https://www.amazon.com/dp/0071360573/?tag=pfamazon01-20
https://www.amazon.com/dp/0596153740/?tag=pfamazon01-20
https://www.amazon.com/dp/0132549867/?tag=pfamazon01-20