draw 3 cards without replacement from a standard 52 card deck. what is the probability that: 1.they...
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Draw 3 cards without replacement from a standard 52 card deck.What is the probability that:
1. They are all red ?
2. At least one is black ?
3. They are all face cards ?
4. They are all red AND they are all face cards ?
5. They are all red OR they are all face cards ?
6. They are all red IF they are all face cards ?
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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
the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22,100 3 x 2 x 1
return to problem
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
the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22,100 3 x 2 x 1
2. At least one is black ?
“at least one black” means “NOT all red”
P( all red ) + P( NOT all red ) = 1
217
1517
1717
1517
+ = return to problem
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
the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22,100 3 x 2 x 1
3. They are all face cards? 220 22,100
there are 12 face cardsking, queen and jack ofhearts, diamonds, clubs and spades
# favorable outcomes = 12 C 3 = 12x11x10 3x2x1
= 220 return to problem
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
the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22,100 3 x 2 x 1
3. They are all face cards? 220 22,100
there are 6 red face cardsking, queen and jack ofhearts and diamonds
# favorable outcomes = 6 C 3 = 6x5x4 3x2x1 = 20
4. They are all red and they are all face cards? 20 22,100
return to problem
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
the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22,100 3 x 2 x 1
3. They are all face cards? 220 22,100
4. They are all red and they are all face cards? 20 22,100
5. They are all red or they are all face cards =
P( R F ) = P( R ) + P( F ) - P( R F )
= 2600 + 220 - 20 = 2800 22100 22100 22100 22100
return to problem
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
the number of possible outcomes = 52 C 3 = 52 x 51 x 50 = 22,100 3 x 2 x 1
3. They are all face cards? 220 22,100
4. They are all red and they are all face cards? 20 22,100
6. They are all red if they are all face cards =
P( R / F ) = P( R F ) = 20/22100 = 20 P( F ) 220/22100 220
return to problem
