For each of the following, assume you are working with a standard deck of 52 cards. There are 13 cards (2,3,4,5,6,7,8,9,10, jack, queen, king and Ace) in each of four suits (Clubs, Diamonds, Hearts, and Spades).
a. What is P(Club) when drawing one card?
b. What is P(Jack) when drawing one card?
c. What is P(Jack n Clubs) when drawing one card?
d. What is P(Jack U Clubs) when drawing one card?
e. What is the P(Jack/Face Card) when drawing one card? This roughly translates to what is the probability of getting a Jack if you know the card is a face card.
f. What is the P(Red/Heart) when drawing one card
Thank you
a. To find the probability of drawing a Club when drawing one card, we need to determine the number of favorable outcomes (number of Clubs) and the total number of possible outcomes (total number of cards in the deck).
Number of Clubs = 13 (since there are 13 Clubs in a standard deck)
Total number of cards = 52 (as there are 52 cards in a standard deck)
Therefore, the probability of drawing a Club is:
P(Club) = Number of Clubs / Total number of cards = 13 / 52 = 1/4
b. To find the probability of drawing a Jack when drawing one card, we follow a similar approach. The number of favorable outcomes (number of Jacks) and the total number of possible outcomes (total number of cards in the deck) are:
Number of Jacks = 4 (since there are 4 Jacks in a standard deck)
Total number of cards = 52
Therefore, the probability of drawing a Jack is:
P(Jack) = Number of Jacks / Total number of cards = 4 / 52 = 1/13
c. The probability of drawing both a Jack and a Club when drawing one card is zero because there is no card that is both a Jack and a Club in a standard deck. Therefore, P(Jack n Clubs) = 0.
d. To find the probability of drawing either a Jack or a Club when drawing one card, we can add the individual probabilities of drawing a Jack and drawing a Club separately, and then subtract the probability of drawing a card that is both a Jack and a Club (which is zero in this case).
P(Jack U Clubs) = P(Jack) + P(Club) - P(Jack n Clubs)
P(Jack U Clubs) = (1/13) + (1/4) - 0
P(Jack U Clubs) = 17/52 = 4/13
e. To find the probability of drawing a Jack given that the card is a face card, we need to determine the number of favorable outcomes (number of Jacks that are face cards) and the total number of possible outcomes (number of face cards).
Number of face cards = 12 (since there are 3 face cards in each suit: Jack, Queen, King)
Number of Jacks (that are face cards) = 1
Therefore, the probability of drawing a Jack given that the card is a face card is:
P(Jack/Face Card) = Number of Jacks (that are face cards) / Number of face cards = 1 / 12
f. To find the probability of drawing a red card given that the card is a Heart, we need to determine the number of favorable outcomes (number of red cards that are Hearts) and the total number of possible outcomes (number of Hearts).
Number of red cards = 26 (since there are 26 red cards in a standard deck: 13 Hearts and 13 Diamonds)
Number of Hearts = 13
Therefore, the probability of drawing a red card given that the card is a Heart is:
P(Red/Heart) = Number of red cards (that are Hearts) / Number of Hearts = 26 / 13 = 2
a. To find the probability of drawing a Club when drawing one card, we need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, there are a total of 52 cards in the deck, and 13 of them are Clubs.
Therefore, the probability of drawing a Club can be calculated as follows:
P(Club) = Number of favorable outcomes / Total number of possible outcomes
P(Club) = 13 / 52
P(Club) = 1/4
So, the probability of drawing a Club when drawing one card is 1/4.
b. To find the probability of drawing a Jack when drawing one card, we again need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, there are still a total of 52 cards in the deck, but there are 4 Jacks.
Therefore, the probability of drawing a Jack can be calculated as follows:
P(Jack) = Number of favorable outcomes / Total number of possible outcomes
P(Jack) = 4 / 52
P(Jack) = 1/13
So, the probability of drawing a Jack when drawing one card is 1/13.
c. To find the probability of drawing both a Jack and a Club when drawing one card, we need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, there is only 1 Jack of Clubs in the deck.
Therefore, the probability of drawing a Jack and a Club can be calculated as follows:
P(Jack n Clubs) = Number of favorable outcomes / Total number of possible outcomes
P(Jack n Clubs) = 1 / 52
P(Jack n Clubs) = 1/52
So, the probability of drawing a Jack and a Club when drawing one card is 1/52.
d. To find the probability of drawing either a Jack or a Club when drawing one card, we need to determine the number of favorable outcomes and the total number of possible outcomes. In this case, there are 4 Jacks and 13 Clubs in the deck, but the Jack of Clubs has already been counted in both groups. Therefore, we subtract 1 from the total count (4 + 13 - 1 = 16).
Therefore, the probability of drawing either a Jack or a Club can be calculated as follows:
P(Jack U Clubs) = Number of favorable outcomes / Total number of possible outcomes
P(Jack U Clubs) = 16 / 52
P(Jack U Clubs) = 4/13
So, the probability of drawing either a Jack or a Club when drawing one card is 4/13.
e. To find the probability of drawing a Jack given that the card is a face card, we need to determine the number of favorable outcomes and the total number of possible outcomes among the face cards. In this case, there are 12 face cards (3 Jacks, 3 Queens, and 3 Kings).
Therefore, the probability of drawing a Jack given that the card is a face card can be calculated as follows:
P(Jack/Face Card) = Number of favorable outcomes / Total number of possible outcomes
P(Jack/Face Card) = 3 / 12
P(Jack/Face Card) = 1/4
So, the probability of drawing a Jack given that the card is a face card is 1/4.
f. To find the probability of drawing a red card given that the card is a Heart, we need to determine the number of favorable outcomes and the total number of possible outcomes among the Hearts. In this case, there are 13 Hearts in the deck, and half of them are red.
Therefore, the probability of drawing a red card given that the card is a Heart can be calculated as follows:
P(Red/Heart) = Number of favorable outcomes / Total number of possible outcomes
P(Red/Heart) = 6 / 13
So, the probability of drawing a red card given that the card is a Heart is 6/13.
a. 1/4
b. 4/52 = 1/13
c. 1/52
d. 13 clubs including jack and 3 other jacks = 16/52
e. 16 face cards , 4 are Jacks 4/16 = 1/4
f if we know we got a heart, it is red 13/13 = 1