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# Secondary Forum

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# Probability

lhooper 07 January 2020 18:49
Posts11
Joined05/01/07

Please can you help settle a disagreement?

Twelve people at a sale all want to buy a TV, but there are only two left. The TVs are allocated at random. What is the probability that one particular person will get one of the TVs?

Is it 2/12 or is it 1/12 + 1/11 ? Or something different ?

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coanem 07 January 2020 21:32
Posts34
Joined03/05/11

Well probability always has the capacity to surprise me, but I think it's (for 2 TVs A and B):

( A ) and (not B given A ) or (B) and (not A given B)

1/12x10/11 + 1/12 x 10/11

Answer would be different if includes possibility of person getting both (depends what you mean by at random)

Interested to hear other views!

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MarkDawes 08 January 2020 16:40
Posts319
Joined09/04/07

Let's be pessimistic.  What's the probability you don't get the first one?  Then, presumably there are only 11 people still in play and ten of them will be unlucky.  What's the probably you don't get the second one?

Now we need to multiply these probabilities, because we think we _won't_ get the first one AND we _won't_ get the second one.

This gives you the probability you will be unlucky and get neither TV.  Now can work out the probability you do get one.

Any use?

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lhooper 08 January 2020 17:19
Posts11
Joined05/01/07

Thank you Mark, that's a nice easy method. I'm the eternal optimist so I'll have to change the way I think!

Thank you for the help! Much appreciated.

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derekrobinson 08 January 2020 17:32
Posts88
Joined25/06/06

The number of ways you can select 2 people from 12 is 12C2 = 66

The number of pairs where you are included is 11

Probability you win a TV 11/66 = 1/6

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lhooper 08 January 2020 17:45
Posts11
Joined05/01/07

Thank you Derek for the optimistic method!

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coanem 09 January 2020 12:45
Posts34
Joined03/05/11

Reconsideration of my earlier : does depend on selection method. If say 12 tickets with 2 drawn from hat, then to win needs:     (win Ticket1) OR (notwin ticket 1 and win ticket 2) , so

1/12  +11/12 x 1/11 = 2/12

However I agree  'pessimistic' method is more elegant!

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lhooper 09 January 2020 13:17
Posts11
Joined05/01/07

Thank you! Another good method.

I did O level maths (before GCSE) followed by A level Pure and Applied, and then into a science degree, without learning any statistics! Where would this probability topic fall in the current curriculum? Is it GCSE or A level?

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