Question

A person tosses a fair coin until she obtains 2 heads in a row. She then tosses a fair die the same number of times as she tossed the coin. What is the expectation and variance for the number of 1s in the sequence of die rolls? How would your answer change if the coin was unfair, and the probability of obtaining heads was p?

Answer 1

The expectation and variance for the number of 1s in the sequence of die rolls is: 1/6

If the coin was unfair the change is: 1/2

The probability of obtainig heads was: 51%

Explanation:

In probability and statistics theory:

The expectation and variance possibilities gotten rolling one dice are six.

In independent Bernoulli trials sequence with probability 1/2 of success on each trial is metaphorically called a fair coin.

By the other hand if the probability is not 1/2, it is called a biased or unfair coin.

It might be thought that the toss of a coin is always a 50/50 probability, with a 50 percent chance it lands on heads, and a 50 percent chance it lands on tails but if it starts out as heads, there's a 51% chance that it will end as heads.