The Student Room Group

I thought this an interesting puzzle

There are 4 playing cards face down on a table

You turn 2 over

The probability that you turn over 2 black cards is 0.5

What is the probability of turning over 2 red cards
Is this is a trick question?
Is it impossible as there's 3 black cards?
Reply 3
Original post by TenOfThem
There are 4 playing cards face down on a table

You turn 2 over

The probability that you turn over 2 black cards is 0.5

What is the probability of turning over 2 red cards


Spoiler

Reply 4
Zero.


Spoiler

Original post by 123formyabc
Is this is a trick question?


I was thinking this too. Is it one of those questions where the answer is that 'it depends'
Reply 6
Original post by UnknownRoyalist
I was thinking this too. Is it one of those questions where the answer is that 'it depends'


It isn't. There are exactly five cases for how many of the four cards are black. Only one of them gives a 50% chance of getting two black cards.
Original post by BlueSam3
It isn't. There are exactly five cases for how many of the four cards are black. Only one of them gives a 50% chance of getting two black cards.


Oh. Makes sense
Reply 8
Original post by BabyMaths

Spoiler



nice though, isn't it
Reply 9
Original post by TenOfThem
nice though, isn't it


I'll use it. :biggrin: Teach the young ones to think before they speak.
Reply 10
Original post by BabyMaths
I'll use it. :biggrin: Teach the young ones to think before they speak.


that was my view to - to much jumping in with an answer and hoping - more step back and think
Original post by TenOfThem
There are 4 playing cards face down on a table

You turn 2 over

The probability that you turn over 2 black cards is 0.5

What is the probability of turning over 2 red cards


Sorry for dragging this thread up. I'm so confusedd how is the probability 0??? surely it's 0.5 :frown:((.
Reply 12
Original post by maths learner
Sorry for dragging this thread up. I'm so confusedd how is the probability 0??? surely it's 0.5 :frown:((.


How can it be

That would mean that the P(1R and 1B) is zero - do you think that is so?
Original post by TenOfThem
How can it be

That would mean that the P(1R and 1B) is zero - do you think that is so?


i'm having a brain freeze moment. How would that mean it's zero? Ugh it's so annoying I always find I can do all the 'harder' maths stuff but then simple things trip me up :/
Reply 14
Original post by maths learner
i'm having a brain freeze moment. How would that mean it's zero? Ugh it's so annoying I always find I can do all the 'harder' maths stuff but then simple things trip me up :/


You have the following possibilities for your 4 cards

RRRR
RRRB
RRBB
RBBB
BBBB

Since you can turn over 2 black, the first 2 can be ignored
Since the P(2B) is not 1 we can ignore the latter

So we have

RRBB
or
RBBB

For each of these work out the P(2B) use a tree diagram maybe?

Which meets the need for P(2B) = 0.5
Reply 15
Original post by maths learner
i'm having a brain freeze moment. How would that mean it's zero? Ugh it's so annoying I always find I can do all the 'harder' maths stuff but then simple things trip me up :/


If you're saying the probability of both 2 black cards is 0.5 and the probability of 2 red cards is also 0.5, then those are the only two possibilities.

Meaning that you believe that when turning over 2 random cards the probability of them being of different colours is 0.
Original post by TenOfThem
You have the following possibilities for your 4 cards

RRRR
RRRB
RRBB
RBBB
BBBB

Since you can turn over 2 black, the first 2 can be ignored
Since the P(2B) is not 1 we can ignore the latter

So we have

RRBB
or
RBBB

For each of these work out the P(2B) use a tree diagram maybe?

Which meets the need for P(2B) = 0.5


RBBB, so then the probability of RR is then 0. Got it! Thank you, that's a nice problem!
Reply 17
Original post by maths learner
RBBB, so then the probability of RR is then 0. Got it! Thank you, that's a nice problem!


:biggrin:
Original post by TenOfThem
:biggrin:


:smile:
It's moments like this I wish I was good at maths:pierre:

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