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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 :

pedrocarratore

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%.

facundo3141592

The probabilities for the given events are:

  • a) 1/2
  • b) 1
  • c) 1/13
  • d) 1/3.

How to find the probabilities?

We assume that all the cards have the same probability of being drawn, so the probability of getting a given card out of the deck is given by the quotient between the number of these types of cards and the total number of cards.

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

There are 13 heart cards and 26 red cards, so the probability is:

p = 13/26 = 1/2 = 0.5

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

There are 13 hear cards, and out of these 13 heart cards there are 13 red cards, so the probability is:

p = 13/13 = 1

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

There are 26 red cards, and 2 of these are kings, so the probability is:

p = 2/26 = 1/13.

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

There are 12 face cards, and 4 of these are queens, so the probability is:

p = 4/12 = 1/3.

If you want to learn more about probability, you can read:

https://brainly.com/question/25870256

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