Question

You flip a fair coin until you see three tails in a row. What is the average number of headsthat you’ll see until gettingTTT?

Answer 1

Answer:

14

Step-by-step explanation:

From the given information:

suppose, Y is the number of times a coin is being flipped.

If the coin is flipped for the first time and we get H, then we have:

TTT = $\dfrac{1}{2}(Y+1)$

Afterward, if we get H, then we waste two times plus the probability of this event $\dfrac{1}{4}$.

Therefore, we have : $\dfrac{1}{4}(Y+2)$

Afterward, if we get H, then we waste three times plus the probability of this event $\dfrac{1}{8}$.

Therefore, we have : $\dfrac{1}{8}(Y+3)$

If we got T at the third time, then;

T = $\dfrac{1}{8}(3)$

Thus, average number of headsthat you’ll see until gettingTTT can be expressed as:

$= \dfrac{1}{2}(Y+1)+ \dfrac{1}{4}(Y+2)+ \dfrac{1}{8}(Y+3)+ \dfrac{1}{8}(3)$

= 14