If I flip a coin 4 times what are the chances that I will get a tail twice in a row?

Question

I mapped it out to be 8/16 but this must be wrong. Is it?

janson, three tails in a row still includes two tails in a row so yes I would include it. What I don't get is that it seems to be a 1/2 chance which would say if I flipped a coin twice it would happen once which is definitely not right so I struggle to get it.

Answer 1

P(tail) on 1st throw = 1/2
P(tail) on 2nd throw = 1/2
P(tail) on 3rd throw = 1/2
P(tail) on 4th throw = 1/2

A = P(1st AND 2nd) = 1/4
B = P(2nd AND 3rd) = 1/4
C = P(3rd AND 4th) = 1/4
P(A OR B OR C) 3/4 - 1/64 = 47/64

Answer 2

MODIFIED AS OF 11/30/2007

I was wrong!!! The probability IS .5. What I wrote below did not take into account overlapping probabilities. There are 16 possibilities, 8 of which will yield success to your answer. I just spent 20 minutes on the phone with my old Statistics Professor (a very energetic and charismatic Egyptian) finding out what I did wrong. You can take it to the bank that it is .5
(50/50) if Dr. Said (pronounced Sigh-eed)says it is so! Disregard what I wrote below.

Each coin flip has a probability of .5 of being a heads.
For multiple probabilities the rule is:
And=multiply, or=add
There are three possibilities for two in a row in four flips:
1st and 2nd, 2nd and 3rd, 3rd and 4th.
So, going back to the rule, you have:
What is the probability that the 1st AND 2nd, OR 2nd AND 3rd, OR 3rd AND 4th flips are heads.

(1) 1st AND 2nd = .5 x .5 = .25
(2) 2nd AND 3rd = .5 x .5 =.25
(3) 3rd AND 4th = .5 x .5 =.25

Since (1), (2) OR (3) is what you are looking for, you
add the above" .25 + .25 + .25 = .75

Answer 3

Hi! I'm not great at statistics, but here goes:
The possible combinatins I can find are:
1. HHHH
2. HHHT
3. HHTT
4. HTTT
5. HTHT
6 HTTH
7. TTTT
8. TTTH
9. TTHH
10. THHH
11. THTH
12. THHT

Of these numbers 3,4,6,7,8,9 include TT (tails twice in a row), so I would make that 6/12, which is interesting because that is a 50/50 chance, the same as you worked out.

I'm not saying this is right - just my best effort, like I said I'm no statistician!!

Answer 4

There is a very simple way to do this problem.
H2 = event of 2 Heads in a row
T2 = event of 2 Tails in a row

P(H2 or T2) = 1 - P(neither)
The only way it neither could occur is THTH or HTHT out of 2^4=16 possible permutations.
P(neither) = 2/16
P(H2 or T2) = 7/8

P(H2 and T2) = P(TTHH or HHTT) = 2/16 = 1/8

P(H2 or T2) = P(H2) + P(T2) - P(H2 and T2)
P(H2) + P(T2) = 7/8 + 1/8 = 1

Now by symmetry, P(H2) = P(T2) = 1/2

Ans. 1/2

*EDIT*
Note that if you flipped the coin just twice, you can use this same method:
P(H2 or T2) = 1 - 2/2^2 = 1/2
P(H2 and T2) = 0
P(H2) + P(T2) = 1/2 + 0 = 2P(T2)
P(T2) = 1/4

You'll find that as the number of tosses increase, the probability of consecutive tails approaches 1.

Answer 5

yes probability is a half (0.5) there are 16 permutations of heads and tails (each equally likely). For all but HTHT & THTH you will have al least one of two consecutive heads or tails. and for all but HHTT & TTHH of the remaining you will have either consecutive heads or tails therefore by symetry you will have half of the remaining consecutive heads and half consecutive tails. Since the no pairs and the both pairs exactly ballance there will be a 50% chance of getting consecutive tails.

Equally you can just workout all the 16 combinations and say whether it complies, half of them (8) will.

Answer 6

total combination=2^4=16
the chances of having 2 tail IN A ROW
is
ttht
tthh
htth
thtt
hhtt
but you cannot have 3 tails in a row by your definition
therefore only 5 chances
probability is 5/16

Answer 7

I think 1/2 is correct, You either have to get it on the first two flips or the last two flips....wait a minute, you could also get it on the two middle flips. 1/4 for each possibility x 3 would be 3/4 chance. That's my guess and I'm stickin' to it.

Answer 8

Lots of wrong answers here.
There are 2*2*2*2=16 possibilities altogether.
Of these, HHTT, HTTH, HTTT, THTT, TTHH, TTHT, TTTH, and TTTT all qualify (total 8).
HHHH, HHHT, HHTH, HTHH, THHH, HTHT, THTH, and THHT don't (total 8).
So the chance is 8/16 = 1/2.
.

Answer 9

50/50?

Answer 10

Bob is correct. 0.75 chance.