Question

The probability of drawing two red cards at random one after the other from a deck containing 52 cards with replacement is which type of event?

• A. $\text{Independent}$
• B. $\text{Dependent}$

Answer 1

The correct option is A $\text{Independent}$

Given,
Number of cards in the deck$=52$

Let A be the event of drawing first red card from deck.

So, probabilty of drawing first red card is $\text{P(A)}=\frac{\text{total favourable outcomes}}{\text{total number of outcomes}}$

$\text{P(A)}=\frac{26}{52}=\frac{1}{2}$

Similarly,
B be the event of drawing second red card after replacing back the first.

So, probabilty of drawing second red card after replacing first is $\text{P(B)}=\frac{\text{total favourable outcomes}}{\text{total number of outcomes}}$

$\text{P(B)}=\frac{26}{52}=\frac{1}{2}$

Clearly, probability of event B is independent of event A because outcome of event B does not depend on outcomes of event A.

So, these events are independent.