
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
15. Twins. The probability of the birth of twins in the country of Schwambrania is $p$, and triplets are not born in Schwambrania.

a) Estimate the probability that a person met on the street in Schwambrania is one of a pair of twins.

b) In a Schwambranian family with three children, what is the probability that there is a pair of twins among them?

c) In Schwambranian schools, twins are always enrolled in the same class. If there are $N$ first-graders in Schwambrania, what is the expected number of pairs of twins among them?

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