There are 13 counters in a bag. 4 counters are red, the rest are blue. Alice takes 2 counters without replacing them. What is the probability that both counters are the same colour?

To begin question, we must establish how blue counters there are at the start. This is a simple subtraction calculation.13-4=9There are 4 red counters and 9 blue counters, which totals to 13 counters. Next, we must note that Alice does not replace the counters after taking them. This means that the events are dependent on each other. Depending on whether it was independent or dependent, that will drastically change our approach to the question.If we imagine both counters were red, then the probability of the first counter being red was 4/13 and the second counter being red will have been 3/12, as there would have been 1 less red counter in the bag. Since this is an “AND” probability, we have to remember to multiply the 2 fractions, getting an answer of 1/13. Now, we have to remember that the question does not specify as certain colour, but only mentions that they need to be the same colour, so we have to do the same for blue as well. The probability of each counters being blue are 9/13 and 8/12 respectively. We multiply the 2 fractions together to get 6/13. We add the 2 fractions (1/13 and 6/13) to get 7/13. Therefore, the probability that both counters are the same colour is 7/13.