Red and Face Cards Probability

This video tutorial covers three counting problems using a standard deck of playing cards. It begins by defining sets of red and face cards, then calculates the union and intersection of these sets. The tutorial explains how to determine the number of ways to select a card that is either red or a face card, both red and a face card, and two cards where the first is red and the second is a face card. The video uses formulas and a Venn diagram to illustrate these concepts, providing a comprehensive understanding of counting principles in probability.

What are the three main questions discussed in the lesson?

• Selecting a number card, a face card, and a joker

• Selecting a red or face card, a red and face card, and two cards with specific conditions

• Selecting a red card, a black card, and a face card

• Selecting a red card, a number card, and a face card

How many red cards are there in a standard deck?

• 39

• 26

• 13

• 52

What is the cardinality of the set of face cards?

• 10

• 12

• 16

• 14

How do you calculate the number of cards that are either red or face cards?

• Add the number of red cards and face cards, then subtract the red face cards

• Add the number of red cards and face cards

• Subtract the number of red cards from face cards

• Multiply the number of red cards by face cards

Why do we subtract the number of red face cards when calculating the union of red and face cards?

• To include all cards in the deck

• To make the calculation easier

• To avoid counting them twice

• To increase the total count

How many cards are both red and face cards?

• 6

• 10

• 8

• 4

What does the intersection of sets A and B represent?

• Cards that are only face cards

• Cards that are neither red nor face cards

• Cards that are either red or face cards

• Cards that are both red and face cards

In the two-card selection problem, what is the first case considered?

• First card is a face card, second is red

• First card is red and a face card, second is a face card

• First card is red but not a face card, second is a face card

• First card is a number card, second is a face card

How many ways can you select two cards where the first is red and the second is a face card?

• 406

• 356

• 306

• 256

What is the total number of face cards left after selecting a red face card?

• 10

• 13

• 11

• 12