
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system

Aboard an airliner, there are $2n$ passengers, and the airline has loaded $n$ chicken meals and $n$ fish meals for them. It is known that a passenger prefers chicken with probability 0.5 and fish with probability 0.5. We call a passenger dissatisfied if they do not get what they prefer.

a) Find the most likely number of dissatisfied passengers.

b) Find the expected number of dissatisfied passengers.

c) Find the variance of the number of dissatisfied passengers.

Present the answer in LaTex format: \boxed{Your answer}
user