These have been dark days indeed in Calvos, since the invasion of the Overumbrians. Some Calvosian cities have surrendered to the brutal attacks of the invaders and now live under martial law, while other areas remain under siege, barely holding on as their supplies dwindle.

The Army of Calvos does its best to hold out against the Overumbrians, but it is much smaller and lacks the more sophisticated weapons of the enemy. But they fight on, struggling to recapture their land through sheer will and determination.

Marlowe is part of The United, a network of patriotic Calvosian spies. She has been working undercover as a chambermaid in the headquarters of the Overumbrian High Commander. Today she overheard the High Commander discussing his plans with his generals.

 

 

"Once we capture the Northwest Coast, there will be no way for the Calvosians to get arms or supplies from overseas. They will have to surrender."

 

"Will we attack by land or sea?"

 

"Here is the plan...."

"I have received word that The United believes that we will attack by sea. Let them believe that. Meanwhile, our troops will approach from other directions and prepare to attack."

 

"Where are there camps located? How will they approach?"

 

 

Silently, our heroine Marlowe crept away as she heard the papers unfolding. It was true! The United did believe that the Overumbians were only planning to attack from the sea. She needed to see those plans and get them to her contact in the town of Stygios.

 

But how can Marlowe succeed?

Marlow needs to break into the High Commander's office.

A guard stands watch over the office every night. Marlow has been watching them carefully.

 

Six of the guards stay awake and remain alert all night. 4 doze off, but will wake up if they hear any noise. 2 fall asleep very heavily and don't wake up until it is almost morning.

 

What is the probability that she will get one of the guards who falls completely asleep?


Is this probability favorable to Marlowe?

 

What is the probability that she will get a guard that is a light sleeper or a heavier sleeper?.


Will waiting change this probability?

 

Express your answers in simplest form.

 

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