This is one of those questions that punish you for overthinking and overanalyzing. The question is "What is the probability of you having the two-headed coin?". The bit about flipping four heads out of four flips is there to throw you off.
Yeah, this is a tricky one. Well based on my Probability course last semester, I would say you would need more information. Basically, like everyone else has said, you would need to know if the probability is the overall one, or the one based on the information given (four heads.) Overall: 25% When you take the information into account: 84%
Probability of an event always means: out of all possible outcomes, what are the chances the event occurred? The information in the question tells us that the only possible outcomes are those which result in the coin landing heads 4 times in a row. Any other outcome would contradict what we know already happened. I think the question in unambiguous; just a bit tricky for those of us rusty with conditional probability.
Yeah, you are probably right. I guess I'm just having a hard time grasping that this would be an interview question, with (I'm assuming) no pen/paper or calculator. I'm pretty sure I could answer a question like this during one of my tests last semester, but I don't know if I could randomly during an interview.
I think it's more of a question to see if you'll even attempt it or walk through it. If you get the answer, you're even more impressive. One of the interview questions I got in my first interview for a "real job" was "how many seconds are there in a year?" Some other interesting ones I've gotten in other interviews were "how many squares are on a chess/checker board?", "how would you weigh an airplane?", "given an alarm clock, how would you find the height of a building?". I'm sure I'm missing some good ones...
Or it may be a trick to see if you say "think outside the box" upon which you will be immediately passed over.
Not true - this is a variation of the Monty Hall question of whether you'd change which door you pick. Most people say you shouldn't, but you actually should. The additional information is relevant. Knowing the outcome of the flips changes what you know about which coin you got. For example, if you had gotten a Tails, you know for sure you didn't have the 2-heads coin.
Quantitative Analyst? So I suppose the interviewer just considered it to be a basic question then. BTW, how did you arrive at your answer 1 / (3/16 + 1). It computes to the right answer, but its not clear to me how you came up with that particular expression. Maybe there's a shorthand way of answering the question I'm not seeing.
