An experiment consists of repeatedly tossing 2 fair coins until the toss results in one each...

An experiment consists of repeatedly tossing 2 fair coins until the toss results in one each of a Head and a Tail. What is the mathematical expectation of the number of times you will need to toss the 3 coins to achieve this?

Expert Solution

Probability of getting a head and tail is because there are 2 ways to get a head and a tail. Also, there are 4 possibilities in total.

Let denote the number of trials it takes to getting the first head and tail. Then can take values 1,2,3,...

Then . This is actually the geometric distribution with parameter .

The mean of this distribution is :

Hence, the mathematical expectation of the number of times the coin needs to be tossed is 2.

orchestra answered 2 years ago

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