
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 Shvambrania is $p$, and triplets are not born in Shvambrania.

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

b) In a certain family from Shvambrania, there are three children. What is the probability that among them there is a pair of twins?

c) In Shvambrania's schools, twins are necessarily enrolled in the same class. There are a total of $N$ first-graders in Shvambrania. What is the expected number of pairs of twins among them?

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