Question

A card is drawn from a well-shuffled deck of 52 cards and then a second card is drawn. Find the probability that the first card is a heart and the second card is a diamond if the first card is not replaced.

Answer 1

Consider the given events.
A = A heart in the first draw
B = A diamond in the second draw

$$\begin{gathered} \mathrm{Now}, \\ P\left(A\right)=\frac{13}{52}=\frac{1}{4} \\ P\left(B/A\right)=\frac{13}{51} \\ \therefore \mathrm{Required}\mathrm{probability}=P\left(A\cap B\right)=P\left(A\right)\times P\left(B/A\right)=\frac{1}{4}\times \frac{13}{51}=\frac{13}{204} \end{gathered}$$