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Probability

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[quote="lunarpower"]
anshumishra wrote:
beat_gmat_09 wrote:
anshumishra wrote:
How does toss being consecutive adds anything to the question ? What is the difference between these two questions :

A coin is tossed 6 times. What's the probability of getting at least 4 heads on consecutive tosses?
vs
A coin is tossed 6 times. What's the probability of getting at least 4 heads ?
definitely not the same -- the default meaning of the former is, without a doubt, "at least 4 heads in a row without interruption". in fact, if you took a poll of native speakers of the english language (who, as far as i understand, are not common on this forum), i would bet decent money that 100% of them would interpret the statement in this way, without any hesitation.
as far as why -- it's probably just the reflex action of assigning an essential modifier to the closest logical thing that it can modify. in that case, that means the immediate assignment of the modifier "on consecutive tosses" to the phrase "at least 4 heads", giving the desired meaning.

of course, if this problem were official, it would almost certainly be phrased in a less bulky, easier-to-understand way, such as "what's the probability of getting at least 4 consecutive heads?"

--

as another example, let's say that you enter a hallway that has a door on the right, and then a door on the left, and then a door on the right, and then a door on the left, etc.
if someone says "go to the third door on the right", you will not go to the third door overall -- you'd count 1, 2, 3 on the right, and you'd ultimately arrive at the fifth door in the hallway.
if that makes sense to you, then the above explanation should make sense as well. (and even if it doesn't, you should still commit that general form of description to memory -- since that's the way those modifiers are going to work, if you see them.)
Thanks Ron for your expert comments on this question !

So to summarize, the OA for the given question is wrong :
Q-> A coin is tossed 6 times. What's the probability of getting at least 4 heads on consecutive tosses?

Correct OA -> 3/32 (See my solution above). This question asks in how many ways one can get at least 4 heads on consecutive tosses .

The given OA would be right for the question :
A coin is tossed 6 times. What's the probability of getting at least 4 heads ?
OA -> 11/32


For the question : A coin is tossed 6 times. What's the probability of getting at least 4 heads on consecutive tosses?

Quote:
beat_gmat_09's comments - The tosses are consecutive, not the heads getting on the tosses !
Tosses being consecutive doesn't add anything to the question (It is understood from the question's first statement), as Ron has confirmed also, it asks for getting at least 4 consecutive heads on tosses.

[/b]

_________________
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Anshu

(Every mistake is a lesson learned )

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[quote="anshumishra"]
lunarpower wrote:
anshumishra wrote:
beat_gmat_09 wrote:
anshumishra wrote:
How does toss being consecutive adds anything to the question ? What is the difference between these two questions :

A coin is tossed 6 times. What's the probability of getting at least 4 heads on consecutive tosses?
vs
A coin is tossed 6 times. What's the probability of getting at least 4 heads ?
definitely not the same -- the default meaning of the former is, without a doubt, "at least 4 heads in a row without interruption". in fact, if you took a poll of native speakers of the english language (who, as far as i understand, are not common on this forum), i would bet decent money that 100% of them would interpret the statement in this way, without any hesitation.
as far as why -- it's probably just the reflex action of assigning an essential modifier to the closest logical thing that it can modify. in that case, that means the immediate assignment of the modifier "on consecutive tosses" to the phrase "at least 4 heads", giving the desired meaning.

of course, if this problem were official, it would almost certainly be phrased in a less bulky, easier-to-understand way, such as "what's the probability of getting at least 4 consecutive heads?"

--

as another example, let's say that you enter a hallway that has a door on the right, and then a door on the left, and then a door on the right, and then a door on the left, etc.
if someone says "go to the third door on the right", you will not go to the third door overall -- you'd count 1, 2, 3 on the right, and you'd ultimately arrive at the fifth door in the hallway.
if that makes sense to you, then the above explanation should make sense as well. (and even if it doesn't, you should still commit that general form of description to memory -- since that's the way those modifiers are going to work, if you see them.)
Thanks Ron for your expert comments on this question !

So to summarize, the OA for the given question is wrong :
Q-> A coin is tossed 6 times. What's the probability of getting at least 4 heads on consecutive tosses?

Correct OA -> 3/32 (See my solution above). This question asks in how many ways one can get at least 4 heads on consecutive tosses .

The given OA would be right for the question :
A coin is tossed 6 times. What's the probability of getting at least 4 heads ?
OA -> 11/32


For the question : A coin is tossed 6 times. What's the probability of getting at least 4 heads on consecutive tosses?

Quote:
beat_gmat_09's comments - The tosses are consecutive, not the heads getting on the tosses !
Tosses being consecutive doesn't add anything to the question (It is understood from the question's first statement), as Ron has confirmed also, it asks for getting at least 4 consecutive heads on tosses.

[/b]
Thank you Smile

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[quote="N:Dure"]
anshumishra wrote:
lunarpower wrote:
anshumishra wrote:
beat_gmat_09 wrote:
anshumishra wrote:
How does toss being consecutive adds anything to the question ? What is the difference between these two questions :

A coin is tossed 6 times. What's the probability of getting at least 4 heads on consecutive tosses?
vs
A coin is tossed 6 times. What's the probability of getting at least 4 heads ?
definitely not the same -- the default meaning of the former is, without a doubt, "at least 4 heads in a row without interruption". in fact, if you took a poll of native speakers of the english language (who, as far as i understand, are not common on this forum), i would bet decent money that 100% of them would interpret the statement in this way, without any hesitation.
as far as why -- it's probably just the reflex action of assigning an essential modifier to the closest logical thing that it can modify. in that case, that means the immediate assignment of the modifier "on consecutive tosses" to the phrase "at least 4 heads", giving the desired meaning.

of course, if this problem were official, it would almost certainly be phrased in a less bulky, easier-to-understand way, such as "what's the probability of getting at least 4 consecutive heads?"

--

as another example, let's say that you enter a hallway that has a door on the right, and then a door on the left, and then a door on the right, and then a door on the left, etc.
if someone says "go to the third door on the right", you will not go to the third door overall -- you'd count 1, 2, 3 on the right, and you'd ultimately arrive at the fifth door in the hallway.
if that makes sense to you, then the above explanation should make sense as well. (and even if it doesn't, you should still commit that general form of description to memory -- since that's the way those modifiers are going to work, if you see them.)
Thanks Ron for your expert comments on this question !

So to summarize, the OA for the given question is wrong :
Q-> A coin is tossed 6 times. What's the probability of getting at least 4 heads on consecutive tosses?

Correct OA -> 3/32 (See my solution above). This question asks in how many ways one can get at least 4 heads on consecutive tosses .

The given OA would be right for the question :
A coin is tossed 6 times. What's the probability of getting at least 4 heads ?
OA -> 11/32


For the question : A coin is tossed 6 times. What's the probability of getting at least 4 heads on consecutive tosses?

Quote:
beat_gmat_09's comments - The tosses are consecutive, not the heads getting on the tosses !
Tosses being consecutive doesn't add anything to the question (It is understood from the question's first statement), as Ron has confirmed also, it asks for getting at least 4 consecutive heads on tosses.

[/b]
Thank you Smile
Thank you as well N:Dure! You have contributed to this thread equally !
Just wanted to summarize the question and the discussions (as this thread already has 4 separate questions going on) !
Very Happy

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Thanks
Anshu

(Every mistake is a lesson learned )

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