How smart are you MPs?

[darktone]

 

[hhiusa]

Well nobody answered my question what's a quarter. Maybe they don't know either.

But anyway, happy you don't disagree with the main point - the more valuable the coin, the more probabible you will lose any competition based on probabibility. Its just like when you get a puncture - it will only ever be when you need to be somewhere in a hurry and that's another well known fact.

A quarter is a quarter dollar. One side has George Washington's face called "heads", the other side has the presidential coat of arms called "tails". The original question is about flipping two quarters and both of them coming up "heads". The answer is 1/4. The probability of two events occuring together is the product of their probabilities.

 

[alexaherself]

Talking of quarters (and who isn't, these days?) ...

... if one coin (A) is weighted so that it comes up heads a quarter of the time, and another (B) weighted so that it comes up heads three quarters of the time, and one of the coins - randomly selected - is flipped twice with both outcomes being "heads", then what was the probability that it was coin B that was flipped?

 

[timsk]

. . . What was the probability that it was coin b that was flipped?

50%

 

[alexaherself]

50%

Would you also have said 50% if the parameters in the question had been that one coin were weighted to come up heads 99% of the time, and the other to come up heads 1% of the time, Tim?

 

[timsk]

Would you also have said 50% if the parameters in the question had been that one coin were weighted to come up heads 99% of the time, and the other to come up heads 1% of the time, Tim?

Yes. The weightings and the number of times the selected coin is flipped are red herrings. It's the (random) selection of the coin in the first place that the question relates to which, as there's just two coins, is a straight 50:50 proposition. I think!

 

[tomorton]

Was it a £1 coin or a 10p coin?

 

[tomorton]

75%

 

[alexaherself]

Would you also have said 50% if the parameters in the question had been that one coin were weighted to come up heads 99% of the time, and the other to come up heads 1% of the time, Tim?

Yes.

Ouch ... I admit I was asking rhetorically, by way of saying "You couldn't possibly think that ..."?

The weightings and the number of times the selected coin is flipped are red herrings. It's the (random) selection of the coin in the first place that the question relates to which, as there's just two coins, is a straight 50:50 proposition. I think!

Er, no ... apologies if the context misled you, guys ... it's not a "trick question". It's a non-trivial probability question ...

75%

Noooooo ... I should have said, in asking the question, something like "By the way, this is a more difficult and complicated question than it appears" ...

 

[alexaherself]

If it puts the question in a better and more appropriate context, you might want to see where I stole it from. The heading and very last question of this little pdf explain further: http://www.maths.cam.ac.uk/sites/ww...14/undergrad/pastpapers/2015/ia/PaperIA_2.pdf :cheesy:

I just happened to be looking at this year's papers, a couple of nights ago (I look at these, each year, when they're published online ), and the word "quarter" just stuck in my mind.

I do have an answer. It's only my own answer (I haven't checked it with an examiner, or anything) but I think it's right, and it isn't 50% or 75%. :|

 

[timsk]

. . . The heading and very last question of this little pdf explain further: http://www.maths.cam.ac.uk/sites/ww...14/undergrad/pastpapers/2015/ia/PaperIA_2.pdf

Whoa, I made the really silly mistake of clicking on your link Alexa! For me, that's worse than an arachnophobia sufferer being forced to watch a heavy duty horror film about giant man eating spiders. On the plus side, I'm thinking it isn't a basic GCSE paper for 16 year olds which, given that my answer is wrong, makes me feel a tad less stupid.

Tim.

 

[alexaherself]

On the plus side, I'm thinking it isn't a basic GCSE paper for 16 year olds

Noooooo, far from it!

My answer is 90% (reasoning follows) ...

The probability of coin A coming up heads twice, from two consecutive flips, is 1/4 x 1/4, which is 1/16.

The probability of coin B coming up heads twice, from two consecutive flips, is 3/4 x 3/4, which is 9/16.

Therefore the hindsight-probability, given random selection from the two alternative coins, is that coin B was 9 times as likely to produce this outcome as coin A, and the chances of it having been coin B are therefore 90%.

I think.

(And the second part of that question is extremely complicated, as is often the case with two-part questions from that source!).

 

[Pat494]

I see The Queen is currently in Malta to host The Commonwealth conference. She could drop in on Alexa's folks for a cuppa ?

 

[NVP]

How smart are your MPs
77% Of British Opposition MPs Couldn't Answer This Simple Math Question About Flipping Coins

Members of parliament were asked what the odds were of getting two heads if you flipped two quarters simultaneously.

47% of Tories got it wrong
77% of Labour got it wrong

I knew there was a reason I supported the Tories.

33% .......right ?

 

[Pat494]

my guess is 1 in 4 times or 25%.

 

[hhiusa]

33% .......right ?

The proability of two events occuring together is represented by the product of their probabilities.

The odds are 1/2 for heads with one quarter and the same for the other quarter.

P(C) = P(A)*P(B) = (1/2)*(1/2) = 1/4

 

[NVP]

Go figure ....