Question

2. Consider drawing a card at random from a standard deck of cards,Part A: Determine the probability that the card is a spade, given that it is black,Part B: Determine the probability that the card is red, given that it is a heart,Part C: Determine the probability that the card is an ace, given that it is black.Part D: Determine the probability that the card is a queen given that it is a face card,

Answer 1

Consider drawing a card at random from a standard deck of cards,

Part A: Determine the probability that the card is a spade, given that it is black,

Part B: Determine the probability that the card is red, given that it is a heart,

Part C: Determine the probability that the card is an ace, given that it is black.

Part D: Determine the probability that the card is a queen given that it is a face card,

we have 52 cards

A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠)

so

Part A: Determine the probability that the card is a spade, given that it is black,

If the card is black, that means the possible outcomes are 26 cards

so

P=13/26

P=0.5

Part B: Determine the probability that the card is red, given that it is a heart,

if the card is a heart, that means, the possible outcomes are 13

so

P=13/13

P=1

because all the cards that are heart are red

Part C: Determine the probability that the card is an ace, given that it is black.

if the card is black the possible outcomes are 26

therefore

P=2/26

P=1/13

Part D: Determine the probability that the card is a queen given that it is a face card