Final answer:
a.) The probability of picking a Jack given that the card is a face card is 1/3. b.) The probability of picking a heart given that the card is a three is 13/4. c.) The probability of picking a red card given that the card is an ace is 13/2. d.) The events Jack and face card are not independent events. e.) The events red card and ace are not independent events.
Step-by-step explanation:
a.) The probability of picking a Jack given that the card is a face card can be calculated by dividing the number of Jacks by the number of face cards. In a standard deck, there are 4 Jacks and 12 face cards. So the probability is 4/12, which simplifies to 1/3.
b.) The probability of picking a heart given that the card is a three can be calculated by dividing the number of hearts by the number of threes. In a standard deck, there are 13 hearts and 4 threes. So the probability is 13/4, which cannot be simplified.
c.) The probability of picking a red card given that the card is an ace can be calculated by dividing the number of red cards by the number of aces. In a standard deck, there are 26 red cards and 4 aces. So the probability is 26/4, which simplifies to 13/2.
d.) The events Jack and face card are not independent events. If a card is already known to be a face card, then the probability of it being a Jack changes. Similarly, the events red card and ace are not independent events. If a card is already known to be an ace, then the probability of it being red changes.