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czarczar
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If six coins are tossed together, what is the probability of not getting the same outcome on consecutive toses.

Guys, I do not have OA. So, do not pounce on me.



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czarczar
If six coins are tossed together, what is the probability of not getting the same outcome on consecutive tosses.

Guys, I do not have OA. So, do not pounce on me.
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Only 2 cases fit the condition:

HTHTHT
THTHTH

Possible Outcomes=2
Total Outcomes=2^6=64
Probability=2/64=1/32

Ans: "1/32"
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Raghava747
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Probability 27 Aug 2011, 12:47
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czarczar
fluke
czarczar
If six coins are tossed together, what is the probability of not getting the same outcome on consecutive tosses.

Guys, I do not have OA. So, do not pounce on me.

Only 2 cases fit the condition:

HTHTHT
THTHTH

Possible Outcomes=2
Total Outcomes=2^6=64
Probability=2/64=1/32

hi fluke thanks for the reply.

I also made these two cases. The way I did try to solve it was that total outcomes =64.

favourable HTHTHT = factorial 6/ fact 3 * fact 3 and same goes for THTHTH.

and it results in 40/64 = 5/8.

could you please tell me what is wrong with my approach?

Ans: "1/32"
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Hello czarczar,

The reason is that the 20 combinations that you get would not adhere to the condition that we have here (no consecutive similar events)

EXAMPLE :
HT HT HT
HT HT TH
HH TT HT
are all combinations that comprise in 20 combinations that you get . Hence Flawed. Similar for TH TH TH
so the combinations possible are only 2/64 = 1/32.

HT HT HT or TH TH TH


Regards,
Raghav.V

Consider Kudos if you feel my explanation was helpful. :-D
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czarczar

hi fluke thanks for the reply.

I also made these two cases. The way I did try to solve it was that total outcomes =64.

favourable HTHTHT = factorial 6/ fact 3 * fact 3 and same goes for THTHTH.

and it results in 40/64 = 5/8.

could you please tell me what is wrong with my approach?
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HTHTHT:
6!/(3!)(3!) will give you number of arrangements of 3 Heads And 3 Tails, but our intention is not that.

With your approach, we'll have all these undesired arrangement considered:
HHHTTT
HHTTTH
TTHHTH
...

20 arrangements like this. And again; when you considered THTHTH, it is again the same thing. 3 T's and 3 H's. We don't want that.

We just want these two arrangements:
THTHTH
HTHTHT
Because only in these 2 arrangements will the Head and Tail alternate and no two consecutive tosses will be same, rest anything will result in at least one consecutive set.

So, the desired arrangements are only 2.

If we talk about possible arrangements, then we have 64 of those.

Probability=Desired/Possible
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czarczar

hi fluke thanks for the reply.

I also made these two cases. The way I did try to solve it was that total outcomes =64.

favourable HTHTHT = factorial 6/ fact 3 * fact 3 and same goes for THTHTH.

and it results in 40/64 = 5/8.

could you please tell me what is wrong with my approach?

HTHTHT:
6!/(3!)(3!) will give you number of arrangements of 3 Heads And 3 Tails, but our intention is not that.

With your approach, we'll have all these undesired arrangement considered:
HHHTTT
HHTTTH
TTHHTH
...

20 arrangements like this. And again; when you considered THTHTH, it is again the same thing. 3 T's and 3 H's. We don't want that.

We just want these two arrangements:
THTHTH
HTHTHT
Because only in these 2 arrangements will the Head and Tail alternate and no two consecutive tosses will be same, rest anything will result in at least one consecutive set.

So, the desired arrangements are only 2.

If we talk about possible arrangements, then we have 64 of those.

Probability=Desired/Possible
Show more


Thanks a lot fluke!!!! :)

Everything is crystal clear now.
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czarczar
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thanks Raghava747. :)
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HTHTHT
THTHTH

number of desirable outcomes = 2
total outcomes = 2^6 = 64

=>desired outcome probability = 2/64 = 1/32



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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Thank you for understanding, and happy exploring!
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