Question

A box contains 6 cards numbered 1 to 6. A student is asked to pick up two cards, one by one after replacement and note down the numbers on the cards. Let $A$ be the event of getting the sum of the numbers on the two cards as 10, and $B$ be the event of a number other than 4 on the first card selected. Find $P(A \text{ and } B)$ and find whether the events $A$ and $B$ are independent events or not.

Hint:

When computing sample spaces with replacement, the denominator is always $n^k$. Always look out for words like "with replacement" or "without replacement" as they entirely alter the conditional probabilities of subsequent events!

Answer 1