Question

2. A card is drawn from a standard deck of 52 cards. Of these events:

- A "the card is a Queen"

- B "the color of the card is red"

- C "the card is a face card"

Which are independent? Explain your answer (especially because I have never played card).

Answer 1

The events A and B are independent

In a deck of cards, there are 4 queen cards of which 2 are red and 2 are black. Number of red cards = number of black cards = 26. Number of face cards = 12 (queen is also a face card)

Two events are independent if P(A) x P(B) = P(A and B)

Proof: P(A) = 4/52 = 1/13

P(B) = 26/52 = 1/2

P(A and B) = 2/52 = 1/26

So, P(A) x P(B) = P(A and B), meaning A and B are independent

The events A and C are dependent

The events B and C are independent

P(B) = 1/2

P(C) = 12/52 = 3/13

P(B and C) = 6/52 = 3/26

So, P(B) x P(C) = P(B and C), meaning B and C are independent