josemnz83 wrote:
On three consecutive flips of a coin, what is the probability that all three produce the same result?
(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2
I came up with (1/2)*(1/2)*(1/2) =1/8
However, the explanation states that the answer is 1/4.
On the Total GMAT book, I had the following question: If a fair coin is flipped three times, what is the probability that it will be heads all three times?
There the answer given is 1/8, which is what I came up with.
Am I missing something? I do not see any distinction between these two questions.
TL;DR
HHH or TTT
Possible Cases: 2
Total Cases: 2^3 = 8
P = 2/8 = 1/4
or P = 1 * 1/2 * 1/2 = 1/4
ANSWER: C
Veritas Prep Official Solution
The trap answer here is 1/8 – you might look at this as a 1/2 probability on the first flip, then a 1/2 on the second, and a 1/2 on the third for a 1/8 probability, but remember – in this case the result of the first flip doesn’t have to be one or the other. Your job is just to match whatever the first result was on the next two. If the first was heads, then you need heads next (a 1/2 chance) and heads again (a 1/2 chance). And if it were tails, then you need tails (1/2) then tails (1/2). But because “any match will do” and you don’t care that it’s a specific match – the question doesn’t specify all heads or all tails, just “all of one of them” – your probability doubles because you’re not concerned about the result of the first event, you’re only concerned about matching whatever that result was.
General Tips
Credit: Veritas Prep
So for probability questions that ask about pairs or matches, remember:
1) Check whether you need a *specific* pair/match or not.
2) If you don’t need a specific pair, but “any pair will do,” then the probability of the first result is 100% – something will happen.
3) If you need to guess, keep in mind that if it’s an unspecified pair/match, it’s almost certain that one of the trap answers will be a smaller number than the correct answer (in the above case, 1/8 is a trap and 1/4 is correct), so you can confidently rule out the smallest number and use number properties to try to eliminate another 1-2 answers.