Question

suppose that you are dealt five cards at random from a standard deck.
what is the probability that AT LEAST four cards will be spades?

Answer 1

at least four means four or five so we have to compute each of these separately

Answer 2

would it be the hypergeometric function but just computed for four and five and then add the two probabilities together?

Answer 3

5 is easiest, it is
\[\frac{13}{52}\times\frac{12}{51}\times \frac{11}{50}\times \frac{10}{49}\times \frac{9}{48}\]

Answer 4

yes you have to add them up

Answer 5

i wrote it out for 5, you can also do it for 4 right?

Answer 6

yeah just when i do the same thing i add the two probabilities up together?

Answer 7

right, and yes you can use hypergeomtric, i just wrote it out like a bonehead. if you use hypergeometric you will have a ton of cancelation and get what i got i am sure

Answer 8

okay sounds good thank you!

Answer 9

think for 4 it will be
\[\frac{\dbinom{13}{4}\dbinom{39}{1}}{\dbinom{52}{5}}\] if i am not mistaken

Answer 10

yw