Two cards are drawn without replacement from a pack of 52 cards. find the probability that the first is a heart and second is red.
My solution goes as follows:
The number of ways of choosing a heart is $\binom{13}{1}$. So, the number of red cards remaining is $25$ as a heart card is already chosen . The number of ways of choosing a red is $\binom{25}{1}$. The number of ways of choosing two cards out of $52$ cards is $\binom{52}{2}$. So the total probabiblity is :$\frac{\binom{13}{1}\binom{25}{1}}{\binom{52}{2}}$
However the answer given is $\frac{25}{204}$. How is this possible? Where is the problem occuring. I am not getting it.
Best Answer
Your numerator and denominator are fundamentally different. Specifically, your numerator implies an order of the cards, but your denominator does not. Try changing your denominator to count the number of cards available to you on your first draw, then the number available on your second draw.