
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 giving birth to twins in Schwambrania is $p$, and triplets are never 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 certain Schwambrania family, there are three children. What is the probability that there is a pair of twins among them?

c) In Schwambrania's schools, twins are always placed in the same class. 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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