Amended my response:

16 possible outcomes from 4 coin tosses.

1 way to get three consecutive heads:

THHH

1 way to get three consecutive tails:

HTTT


[spoiler](B)2/16 [/spoiler]

runzun wrote:Math (PS)

John throws a coin until a series of three consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fourth throw?

(A) 1/16
(B)2/16
(C) 3/16
(D) 6/16
(E) 6/16

can you mention what is for choice E?

I think should be 10/16 or 5/8.

The person will throw the coins until he receives three consec. tails or heads.

case 1) if he gets head or tail in first three throws.
2/8
case 2) if he gets head in first throw & three consec tails in next three throws & vice versa
2/16

so prob. that game will end after fourth throw = 1- prob that game will end before or on fourth throw
= 1-(2/8 + 2/16) = 10/16 = 5/8

user123321

oa is b

runzun wrote:Math (PS)
John throws a coin until a series of three consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fourth throw?

After reading the question, I thought that John is going to continue throwing the coin, until he gets three heads or three consecutive tails. And we are asked to find probability of his game ending after fourth throw. I am confused with the wording. Is it just me? O.o

Maybe the proper wording should be, John threw a coin four times, what is the probability that his game ends after the fourth throw.

user123321

user123321 wrote:

runzun wrote:Math (PS)
John throws a coin until a series of three consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fourth throw?

After reading the question, I thought that John is going to continue throwing the coin, until he gets three heads or three consecutive tails. And we are asked to find probability of his game ending after fourth throw. I am confused with the wording. Is it just me? O.o

Maybe the proper wording should be, John threw a coin four times, what is the probability that his game ends after the fourth throw.

user123321

I misread it the first time, but the wording is actually clear. It's asking for the probability of

THHH or HTTT in 4 tosses.

case 1) if he gets head or tail in first three throws.
2/8
case 2) if he gets head in first throw & three consec tails in next three throws & vice versa
2/16

@ user, even if you consider all Heads or all tails in the first three throws, the probablity would be 1/8. how can it be 2/8.
It should be the product of (1/2)*(1/2)*(1/2).

shekhar.kataria wrote:

case 1) if he gets head or tail in first three throws.
2/8
case 2) if he gets head in first throw & three consec tails in next three throws & vice versa
2/16

@ user, even if you consider all Heads or all tails in the first three throws, the probablity would be 1/8. how can it be 2/8.
It should be the product of (1/2)*(1/2)*(1/2).

I assumed from question that once he gets three consecutive heads or three consecutive tails, he will stop playing.

so in my case when he throws three coins and stops the game, the probability will be 2/8
because TTT or HHH are the only possibilities available.

For my non native ear, that was my understanding. But as mentioned by chieftang, it should better be answered assuming he throws 4 times. And also for the reason that my answer is not among the options

user123321