Question

I flip a coin 6 times. What is the expected number of pairs of consecutive tosses that come up with heads? Example: the sequence HHTHHH has 3 pairs of consecutive HH's.​

Answer 1

Your answer :-

6 fair coins are tossed in a row, so we expect to get sequences that look like:

HHTHTT, THTHHT, HTHTTH, etc.

There are 5 places where consecutive HH pairs can occur, in the first two spots, the second and third spots, the third and fourth, the fourth and fifth, and the last two spots.

At each of these places, the odds of a HH pair occurring is the chance of two independent coins both showing heads. Since each has a 1/2 chance, the total chance is 1/4.

The five places where a HH can occur are not independent of each other, a head in one spot might help create two pairs, but it doesn’t matter for working out expectation. Since there are 5 opportunities, each with a 1/4 chance, the expected number of successes is 5 * 1/4 = 1.25.

So we expect to get 1.25 consecutive HH pairs.

hope it helps ♡

Answer 2

Answer:

Step-by-step explanation: