MAT Exam 2023 Paper

Concept:Each draw is independent because the card is replaced.The probability of each colour is equal on every draw.Explanation:There are two equally likely ways to get different colours: red then black, or black then red.$P(\text{Red}) = \frac{26}{52} = \frac{1}{2}$ and $P(\text{Black}) = \frac{1}{2}$.Since the first card is replaced, the second draw is independent of the first.$P(\text{Red then Black}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$.$P(\text{Black then Red}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$.Therefore, required probability $= \frac{1}{4} + \frac{1}{4} = \frac{1}{2}$.Answer:$\frac{1}{2}$, i.e. Option A.