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.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@Gurome wrote:Let us assume that the coin is fair one.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.
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,Statement 1: n can be either 1 or 2 --> NOT sufficient
- For n = 1 : H and T
For n = 2 : HH, HT, TH, and TT
- P(h) = 1/2
P(T) = 1/2For n = 3 : HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT
- P(h) = 2/4 = 1/2
P(T) = (2/4 + 1/4) = 3/4
- P(h) = 3/8
P(T) = (3/8 + 3/8 + 1/8) = 7/8
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.
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.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?
Anurag@Gurome wrote: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.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?
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.
Please refer to what I have mentioned in the beginning of my analysis...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?
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.
Anurag@Gurome wrote:Please refer to what I have mentioned in the beginning of my analysis...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?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.
GmatKiss wrote:exactly, a coin is treated unfair when it is not mentioned as fair
IMO:E
Yes, the answer should be E as I have mentioned earlier.pemdas wrote:that's what I mean, answer must be E?
we are not given the condition of fair/unfair
please confirm
