Okay, so, my teacher gave us this worksheet of "harder/unusual probability questions", and Q.5 is real tough. I'm studying at GCSE level, so it'd be appreciated if all you stellar mathematicians explained it in a way that a 15 year old would understand. Thanks!So, John has an empty box. He puts some red counters and some blue counters into the box.The ratio of the number of red counters to blue counters is 1:4Linda takes out, at random, 2 counters from the box.The probability that she takes out 2 red counters is 6/155How many red counters did John put into the box?

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Okay, so, my teacher gave us this worksheet of &quot;harder/unusual probability questions&quot;, and Q.5 is real tough. I&#039;m studying at GCSE level, so it&#039;d be appreciated if all you stellar mathematicians explained it in a way that a 15 year old would understand. Thanks!So, John has an empty box. He puts some red counters and some blue counters into the box.The ratio of the number of red counters to blue counters is 1:4Linda takes out, at random, 2 counters from the box.The probability that she takes out 2 red counters is 6/155How many red counters did John put into the box?

lavintisqpsnb · Accepted Answer

The rule of thumb in probability is that the word and implies multiplication, and or implies addition. Seeing as Linda is picking one red counter and one red counter, you know that its going to be the two probabilities of a red counter being picked multiplied by each other.From here, lets call the number of red counters   r, the number of blue counters   b and the total number of counters   r  +  b. Given this, initially there was a             r              r        +        b             chance of picking a red counter, and the next time there was a                     r        −        1                    r        +        b        −        1             chance of picking a red counter (I&#039;m assuming Linda has not replaced the red counter she took out initially). Given this, you can infer:      r          r      +      b        ⋅            r      −      1              r      +      b      −      1        =      6    155  from here, before simplifying anything, you know (for the ratio) that             r      b        =          1      4      , which is useful because it implies that       b    =    4    r  , and hence the question becomes:      r          r      +      4      r        ⋅            r      −      1              r      +      4      r      −      1        =      6    155        1    5    ⋅            r      −      1              5      r      −      1        =      6    155              r      −      1              25      r      −      5        =      6    155    155  r  −  155  =  150  r  −  30  5  r  =  125  r  =  25hence there are 25 red counters in the box. I completed my GCSEs last year, and as far as I&#039;m concerned this should all make sense to you.P.S; which exam board are you sitting? Edexcel by any chance?

Okay, so, my teacher gave us this worksheet of "harder/unusual probability questions", and Q.5 is re

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