Question

You draw a card at random from a standard deck of 52 cards. Find the following conditional probabilities: a.) The probability that a card is a heart, given that it is red? b.) The probability that a card is red, given that it is a heart? c.) Th probability that a card is a king, given that it is red? d.) The probability is a queen, given that it is a face card?

Answer 1

Answer:

a.) 1/2 or 50%

b.) 1/1 or 100%

c.) 1/13 or 7.69%

d.) 1/3 or 33.33%

Step-by-step explanation:

a.) The probability that a card is a heart, given that it is red?

There are four suits in a deck, two of which are red: hearts and diamonds. Since the number of hearts and diamonds is the same, the probability of the card being a heart, given that it is red is 1/2 or 50%.

b.) The probability that a card is red, given that it is a heart?

All hearts are red cards, therefore, given the card is a heart, there is a 1/1 or 100% probability that it is red.

c.) The probability that a card is a king, given that it is red?

There are 26 red cards, 2 of which are kings. Therefore, the probability of a card being a king, given that it is red is 1/13 or 7.69%.

d.) The probability is a queen, given that it is a face card?

There are 12 face cards in a deck, 4 of which are queens. Therefore, the probability of a card being a queen, given that it is a face card is 4/12 or 1/3 or 33.33%.