What is the difference

What is the difference in these two problems [in meaning]?

1. What is the probability of getting at least 2 heads in a row on three flips of a fair coin?
This one asks about the following possible scenaiors:
Case 1
First flip - Heads
Second flip - Heads
Third Flip - Heads

Case 2
First flip - Heads
Second flip - Heads
Third Flip - Tails

Case 3
First flip - Tails
Second flip - Heads
Third Flip - Heads

2. What is the probability of getting at least 2 heads on three flips of a fair coin?
This one talks about getting 2 or more heads on a total of 3 flips (BUT it does not care about them being in a row or back to back). So a possible scenario that this could have, that the other one isnt asking for would be:

First flip - Heads
Second flip - Tails
Third Flip - Heads

Does that help?

akhp77 wrote:What is the difference in these two problems [in meaning]?

1. What is the probability of getting at least 2 heads in a row on three flips of a fair coin?

2. What is the probability of getting at least 2 heads on three flips of a fair coin?

1. What is the probability that you will get 2 heads together on 3 flips.
---> so HHT or HHT --> you cannot have HTH because the 2 heads are not together.

2. Here you still want 2 heads, but they dont have to occur together.
----> so you can have HHT, HTH, THH.

I hope that clarifies!

Gurpinder wrote:

akhp77 wrote:What is the difference in these two problems [in meaning]?

1. What is the probability of getting at least 2 heads in a row on three flips of a fair coin?

2. What is the probability of getting at least 2 heads on three flips of a fair coin?

1. What is the probability that you will get 2 heads together on 3 flips.
---> so HHT or HHT --> you cannot have HTH because the 2 heads are not together.

2. Here you still want 2 heads, but they dont have to occur together.
----> so you can have HHT, HTH, THH.

I hope that clarifies!

@ Gurpinder - 1 says 'at least'.. You missed the HHH scenaio I think.. Or I understood this wrong.

beatthegmatinsept wrote:

Gurpinder wrote:

akhp77 wrote:What is the difference in these two problems [in meaning]?

1. What is the probability of getting at least 2 heads in a row on three flips of a fair coin?

2. What is the probability of getting at least 2 heads on three flips of a fair coin?

1. What is the probability that you will get 2 heads together on 3 flips.
---> so HHT or HHT --> you cannot have HTH because the 2 heads are not together.

2. Here you still want 2 heads, but they dont have to occur together.
----> so you can have HHT, HTH, THH.

I hope that clarifies!

@ Gurpinder - 1 says 'at least'.. You missed the HHH scenaio I think.. Or I understood this wrong.

Yes, you are right!!!! But I wasn't trying to list all possibilities; rather just give examples because akhp77 said he wanted help with the meaning.

Finally, I understood this way

1. What is the probability of getting at least 2 heads in a row on three flips of a fair coin?

Whatever comes [H>=2] in consecutive three flips.

HHT, THH, HHH,


2. What is the probability of getting at least 2 heads on three flips of a fair coin?

Here includes all possibilities.
HHH, HHT, HTH, THH

Am I right.

No. In Q1. in a row is crucial. So the Heads have to be consecutive.

HHT, THH, HHH --- in these at least 2 heads are in a row.

Q2. Heads doesn't have to be consecutive but should have at least 2 Heads.

HTH -- in this 2 heads are separated by a Tail. and other possibilities THH,HHT,HHH.

akhp77 wrote:Finally, I understood this way

1. What is the probability of getting at least 2 heads in a row on three flips of a fair coin?

Whatever comes [H>=2] in consecutive three flips.

HHT, THH, HHH,


2. What is the probability of getting at least 2 heads on three flips of a fair coin?

Here includes all possibilities.
HHH, HHT, HTH, THH

Am I right.

Your almost getting there buddy!!

1. What is the probability of getting at least 2 heads in a row on three flips of a fair coin?

The key to this problem are the words "in a row".

All this means is that the 2 heads HAVE TOO come up TOGETHER. You can't have HTH -- because the 2 heads are seperated by the T. Therefore, you can have HHT or THH < - in either case the 2 heads are together.

2. What is the probability of getting at least 2 heads on three flips of a fair coin?

For this you, the heads DO NOT need to come up TOGETHER. So all you need would be 2 heads but can be in any position. HHT, HTH, THH, HHH.

So you are absolutely right on this one.

I hope that helps!