Question

A bag contains 10 coloured counters. 2 are picked at random. Probability of them both being red is 2/15. Use algebra to work out how many of the 10 counters in the are red?

Answer 1

4

Explanation:

Let's first work this forwards, then we can try working out our question (which will in essence be working backwards).

If I have 10 markers and 5 of them are red, on the first draw we'll have the probability of picking red is `5/10=1/2`

And the second draw has a probability of picking red is `4/9`, giving the probability of picking two red:

`1/2xx4/9=4/18=2/9`

To work backwards then, we have a probability of `2/15`. To find the number of red counters, let's first set the initial number of red counters to be `r`. On the second draw, there is one less red counter, and so `r-1`. This gives:

`r/10xx (r-1)/9=2/15`

Now let's solve for `r`:

`(r^2-r)/90=2/15=12/90`

`:. r^2-r=12`

`r^2-r-12=0`

`(r-4)(r+3)=0`

`=> r=4, -3`

Since we certainly don't negative counters, we start with 4 red counters:

`4/10xx3/9=2/5xx1/3=2/15 color(white)(000)color(green)root`