If positive integer n

Question

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

abhimahna · Answer

IMO answer should be C.

We know that n <=3 => n =1,2 or 3

Statement 1 : P(Exactly once Head) = 1/2

if n = 1, then also the condition is satisfied.
if n = 2, we can have HT,TH,HH,TT. So, exactly once head is two times out of the four. hence, here also, we have probability of exactly once head = 1/2. Hence, insufficient.
For, n =3, we will get exactly one head for 3 cases out of 8, this scenario won't work.

Statement 2 : P(At least one tail) > 1/2.

For n=1,P( at least one tail) = 1/2. hence, this scenario will be invalid.

For n=2 and n=3, we will get a valid scenario. Hence, two values of n. Insufficient.

Combing, only value of n that will work is n=2. Hence, Sufficient.

chesstitans · Answer

st1 tells that n can be either 1 or 2
st2 indicates that n can be 2 or 3.

=> C

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If positive integer n<=3 and n is the number of times a coin is flippe

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