IMO:E

we may have at least no event and at most three events
st(1) tells us that P(heads, once)=1/2 which means that if we flip the coin one time we get 50% chance of heads. This is Not Sufficient, as we need to know how many times the coin was flipped.
st(2) tells us that P(tail, once)+P(tail,twice)+P(tail,thrice)>1/2. This is Not Sufficient, as we know three events' chain but we don't know if the coin is fair (i.e. 50/50) or unfair.
combined st(1&2) Must be Not Sufficient, know P(tail, once)=1-P(heads, once)=1/2 and since the events are independent (two sides may not happen together) we further infer P(tail,twice)=(1/2)^2 and P(tail,thrice)=(1/2)^3. Taken together gives us 1/2 + 1/4 + 1/8 = (4+2+1)/8 = 7/8 for three events which > 1/2
one event will give us =1/2
two events will give us 1/2 + 1/4 = (2+1)/4 >1/2
still unclear two or three events took place

e

take a look st st(2) alone again and see how Insufficient this is, as P(a)>1/2 can be true for both unfair and fair coins {7/8, 6/8, 5/8 ...}

kavn wrote:If positive integer n<=3 and n is the number of times a coin is flipped, what is the value of n ?

1 - The probability of getting heads exactly once is 1/2.
2 - The probability of getting at least one tail is greater than 1/2.

@Anurag, if I don't misread the st(1) it says P(heads, once)=1/2 and doesn't specify the number of events

how you qualify st(1)==> 1 or 2 events and then decide about st(2) 2 or 3 events? (the same in my solution, this isn't Sufficient)

P(at least one tail) can be 3/4 and 7/8 both are greater than 1/2

hence E?

Anurag@Gurome wrote:

kavn wrote:If positive integer n<=3 and n is the number of times a coin is flipped, what is the value of n ?

1 - The probability of getting heads exactly once is 1/2.
2 - The probability of getting at least one tail is greater than 1/2.

Let us assume that the coin is fair one.
If the coin is an unfair one, then we cannot determine the value of n from given informations and the correct answer will be E.


Value of n can be either 1, 2, or 3.
Say, probability of getting exactly one head = P(h)
And, probability of getting atleast one tail = P(T)

Now, possible outcomes and related probabilities,

• For n = 1 : H and T
  • P(h) = 1/2
    P(T) = 1/2
  For n = 2 : HH, HT, TH, and TT
  • P(h) = 2/4 = 1/2
    P(T) = (2/4 + 1/4) = 3/4
  For n = 3 : HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT
  • P(h) = 3/8
    P(T) = (3/8 + 3/8 + 1/8) = 7/8

Statement 1: n can be either 1 or 2 --> NOT sufficient

Statement 2: n can be either 2 or 3 --> NOT sufficient

1 & Together: Only possible value for n is 2 --> Sufficient

The correct answer is C.

omg, you have assumed that the coin is fair ???

how st(1) can't tell you both that the coin is fair and the number of events

it can be that the coin is fair the number of events are limited to 1 and 2 (your case)

but what if the coin isn't fair? where in the question it was specified that the coin is fair?

Anurag@Gurome wrote:

pemdas wrote:@Aunrag, if I don't misread the st(1) it says P(heads, once)=1/2 and doesn't specify the number of events

how you qualify st(1)==> 1 or 2 events and then decide about st(2) 2 or 3 events?

Because from my initial analysis, probability of getting head exactly once is equal to 1/2 only for n = 1 or n = 2. For n = 3, the probability is 3/8 < 1/2. Hence, only n = 1 and n = 2 satisfy statement 1.

And probability of getting at least one tail for n = 2 and n = 3 are 3/4 and 7/8 respectively, both are greater than 1/2. But for n = 1, the probability = 1/2 which is not greater than 1/2. Hence, only n = 2 and n = 3 satisfy statement 2.

Therefore, only n = 2 satisfies both the conditions.

Hope that helps.

that's what I mean, answer must be E?
we are not given the condition of fair/unfair
please confirm

Anurag@Gurome wrote:

pemdas wrote:omg, you have assumed that the coin is fair ???
...
but what if the coin isn't fair? where in the question it was specified that the coin is fair?

Please refer to what I have mentioned in the beginning of my analysis...

Anurag@Gurome wrote:Let us assume that the coin is fair one.
If the coin is an unfair one, then we cannot determine the value of n from given informations and the correct answer will be E.

exactly, a coin is treated unfair when it is not mentioned as fair

IMO:E

it would be treated fair or unfair (uncertain) by making two statements Not Sufficient and suggesting E. Still pending on OA and final say by expert(s)

GmatKiss wrote:exactly, a coin is treated unfair when it is not mentioned as fair

IMO:E