Draw 3 cards without replacement from a standard

Draw 3 cards without replacement from a standard 52 card deck. What is the probability that: 1. They are all red ? answer 2. At least one is black ? 3. They are all face cards ? answer 4. They are all red AND they are all face cards ? answer 5. They are all red OR they are all face cards ? answer 6. They are all red IF they are all face cards ? answer

the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22, 100 3 x 2 x 1 Draw 3 cards without replacement from a standard 52 card deck. What is the probability that: 2, 600 = 2 1. They are all red ? 22, 100 17 there are 26 red cards in a deck so the number of favorable outcomes = 26 C 3 = 26 x 25 x 24 = 2600 3 x 2 x 1 return to problem

the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22, 100 3 x 2 x 1 Draw 3 cards without replacement from a standard 52 card deck. What is the probability that: 2, 600 = 2 1. They are all red ? 22, 100 17 2. At least one is black ? 15 17 “at least one black” means “NOT all red” P( all red ) + P( NOT all red ) = 1 2 17 + 15 17 = 17 17 return to problem

the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22, 100 3 x 2 x 1 Draw 3 cards without replacement from a standard 52 card deck. What is the probability that: 2, 600 1. They are all red ? 22, 100 3. They are all face cards? 220 22, 100 there are 12 face cards king, queen and jack of hearts, diamonds, clubs and spades # favorable outcomes = 12 C = 220 3 = 12 x 11 x 10 3 x 2 x 1 return to problem

the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22, 100 3 x 2 x 1 Draw 3 cards without replacement from a standard 52 card deck. What is the probability that: 2, 600 1. They are all red ? 22, 100 3. They are all face cards? 4. They are all red and they are all face cards? 20 22, 100 there are 6 red face cards king, queen and jack of hearts and diamonds # favorable outcomes = 6 C return to problem = 20 3 = 6 x 5 x 4 3 x 2 x 1

the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22, 100 3 x 2 x 1 Draw 3 cards without replacement from a standard 52 card deck. What is the probability that: 2, 600 4. They are all red and they are all 1. They are all red ? 22, 100 face cards? 20 22, 100 3. They are all face cards? 220 22, 100 5. They are all red or they are all face cards = P( R F ) = P( R ) + P( F ) - P( R F ) = 2600 22100 + 220 22100 - 20 22100 = 2800 22100 return to problem

the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22, 100 3 x 2 x 1 Draw 3 cards without replacement from a standard 52 card deck. What is the probability that: 2, 600 4. They are all red and they are all 1. They are all red ? 22, 100 face cards? 20 22, 100 3. They are all face cards? 220 22, 100 6. They are all red if they are all face cards = P( R / F ) = P( R F ) P( F ) = 20/22100 220/22100 = 20 220 return to problem