
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
14. Suitcases at the airport. A total of 200 suitcases were loaded onto a plane. After the flight, passengers are waiting for their suitcases on the conveyor belt. As soon as the conveyor starts working, a loader begins placing the suitcases on it one by one every two seconds in a random order (as they were brought). Among the passengers, there is a group of businesspeople waiting for their 10 suitcases.

a) (8th-grade level, 3 points). Find the probability that after the conveyor starts, the businesspeople will have to wait exactly two minutes for their last suitcase.

b) (9th-grade level, 3 points). Find the expected value of the random variable "time that businesspeople will have to wait for the last suitcase."

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