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

14

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 =
`(1)/(2)(Y+1)`

Afterward, if we get H, then we waste two times plus the probability of this event
`(1)/(4)`.

Therefore, we have :
`(1)/(4)(Y+2)`

Afterward, if we get H, then we waste three times plus the probability of this event
`(1)/(8)`.

Therefore, we have :
`(1)/(8)(Y+3)`

If we got T at the third time, then;

T =
`(1)/(8)(3)`

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

`= (1)/(2)(Y+1)+ (1)/(4)(Y+2)+ (1)/(8)(Y+3)+ (1)/(8)(3)`

= 14