Asked by Jay
If 4 cards are drawn at random from a standard deck of cards, what are the odds, or probability, that the first three will be of the same suit and the fourth of another suit?
Answers
Answered by
MathMate
First card: any card (52/52)
Second card: one of 12 remaining cards of the same suit (12/51)
third card: one of 11 remaining cards of the same suit (11/50)
fourth card: one of 39 cards of any other suit (39/49)
Since all these are required events, use the multiplication rule to get the combined probability of all four events happening.
Odds are P(E)/(1-P(E)) where P(E) is the probability of an event taking place.
Second card: one of 12 remaining cards of the same suit (12/51)
third card: one of 11 remaining cards of the same suit (11/50)
fourth card: one of 39 cards of any other suit (39/49)
Since all these are required events, use the multiplication rule to get the combined probability of all four events happening.
Odds are P(E)/(1-P(E)) where P(E) is the probability of an event taking place.