I had this question on my mind. I want to know if I am using the correct idea and process.
Find the probability of picking 2 letters one after another from a bag containing all the letters in the alphabet so that they turn out to be 'X' and 'Y' in any order.
First lets pick a letter. We need an 'X' or a 'Y'. But in the second turn there are only 25 cards left, and we need to pick a 'Y' if we picked 'X' the first time and vice versa. So according to me the probability should be:
$$P(n) = \frac{2}{26} * \frac{1}{25} = \frac{1}{325}$$
Am I right? Am I doing it the right way?
Best Answer
Scetch of your correct thinking:
Let $L_1$ denote the first letter that is picked and $L_2$ the second. Then: $$P\left(\left\{ L_{1},L_{2}\right\} =\left\{ X,Y\right\} \right)=$$$$P\left(L_{1}\in\left\{ X,Y\right\} \right)P\left(L_{2}\in\left\{ X,Y\right\} \mid L_{1}\in\left\{ X,Y\right\} \right)=\frac{2}{26}\frac{1}{25}$$